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    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019e18df-79c7-7d06-9036-d1022268c538_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019e18df-7903-7255-8593-77c88f305eb9_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income attributable to Kestrel common shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
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    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019e18df-7a57-732f-9678-e9a4f100c64b_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal Amount</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019e18df-79c7-74c6-ae32-ede5bb614d7a_verboseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity method investments with fair value option elected</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019e18df-79c7-7857-8d57-68f2b27f810b_netLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total unfunded commitments on equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019e18df-79c7-7633-bc92-8a90d8ef8ee0_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extell Hudson Waterfront Holdings</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsMember" xlink:to="lab_us-gaap_EquityMethodInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_019e18df-79c7-78eb-bd70-f63d857989c0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale Securities [Table]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
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    <link:label id="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock_019e18df-7903-7609-a270-b8e285a61093_terseLabel_en-US" xlink:label="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Prior Year Loss Development for the AmTrust Reinsurance Legacy Operations</link:label>
    <link:label id="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock_label_en-US" xlink:label="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of prior year loss development by line of business [Table Text Block]</link:label>
    <link:label id="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock_documentation_en-US" xlink:label="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of prior year loss development by line of business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:href="kg-20260630.xsd#kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock"/>
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    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019e18df-7903-7479-ac61-f2d7636f4c35_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019e18df-7903-7791-b1b5-ba690c703d09_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
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    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Adjustment Criteria, Loss Ratio Floor</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Adjustment Criteria, Loss Ratio Floor</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings_019e18df-79c7-7d0e-a02d-6a1913e50ec3_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quarterly brokerage fee, above portfolio threshold, percent of average holdings</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Quarterly Brokerage Fee, Above Portfolio Threshold, Percent of Average Holdings</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Quarterly Brokerage Fee, Above Portfolio Threshold, Percent of Average Holdings</link:label>
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    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_019e18df-79c7-7408-901b-2f2ac3a8637e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Estimated Aggregate Amortization Expense</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums_019e18df-7a57-71c1-a8b5-b7f8ed0f1ce5_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unearned premiums</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Unearned Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInUnearnedPremiums"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:to="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy_019e18df-79c7-71c5-b561-6a52930f6d5e_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance, amount retained, per policy</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Amount Retained, Per Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:to="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DiversifiedLegacySegmentMember_019e18df-79c7-71c8-a4fa-93a52b0e5854_verboseLabel_en-US" xlink:label="lab_kg_DiversifiedLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diversified Legacy Reinsurance</link:label>
    <link:label id="lab_kg_DiversifiedLegacySegmentMember_label_en-US" xlink:label="lab_kg_DiversifiedLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Diversified Legacy Segment [Member]</link:label>
    <link:label id="lab_kg_DiversifiedLegacySegmentMember_documentation_en-US" xlink:label="lab_kg_DiversifiedLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Diversified Legacy Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiversifiedLegacySegmentMember" xlink:href="kg-20260630.xsd#kg_DiversifiedLegacySegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DiversifiedLegacySegmentMember" xlink:to="lab_kg_DiversifiedLegacySegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromLoansReceivable_019e18df-79c7-773b-aa73-3f3f9cf1c3ae_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net loan receivable from related party</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromLoansReceivable_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForProceedsFromLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:to="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_019e18df-79c7-7eed-bbd5-00acf438006e_negatedTerseLabel_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of earn out liability</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_019e18df-79c7-7033-ab22-2fdaf0e9b932_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of earn out liability</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_label_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Earn-Out, Liability</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability_documentation_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Earn-Out Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability" xlink:href="kg-20260630.xsd#kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability" xlink:to="lab_kg_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentEarnOutLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_019e18df-7a58-7f77-8053-d711590dfe06_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of premiums written, net of cost of unaffiliated inuring reinsurance from related party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Premium Written, Net of Cost of Unaffiliated Inuring Reinsurance From Related Party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Premium Written, Net of Cost of Unaffiliated Inuring Reinsurance From Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:to="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_019e18df-79c7-74f7-8475-e5913adb999b_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_019e18df-7a57-716c-803d-3c6520c0b27a_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares acquired, average cost (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_label_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Acquired, Average Cost Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockAcquiredAverageCostPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:to="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesAmortizedCostBasis_019e18df-79c7-72ab-a442-107ab60d4aa1_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_kg_FixedMaturitiesAmortizedCostBasis_label_en-US" xlink:label="lab_kg_FixedMaturitiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Amortized Cost Basis</link:label>
    <link:label id="lab_kg_FixedMaturitiesAmortizedCostBasis_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Amortized Cost Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesAmortizedCostBasis" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesAmortizedCostBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesAmortizedCostBasis" xlink:to="lab_kg_FixedMaturitiesAmortizedCostBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019e18df-79c7-7020-98dc-956f2162632f_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_019e18df-79c7-7bfa-aae0-97d6f74037b6_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of ceded underwriting risk in exchange for ceding fee</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Ceded Underwriting Risk in Exchange for Ceding Fee</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Ceded Underwriting Risk in Exchange for Ceding Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:to="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustQuotaShareMember_019e18df-79c7-704d-879c-c9eef1c11e4e_terseLabel_en-US" xlink:label="lab_kg_AmTrustQuotaShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share</link:label>
    <link:label id="lab_kg_AmTrustQuotaShareMember_label_en-US" xlink:label="lab_kg_AmTrustQuotaShareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share [Member]</link:label>
    <link:label id="lab_kg_AmTrustQuotaShareMember_documentation_en-US" xlink:label="lab_kg_AmTrustQuotaShareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustQuotaShareMember" xlink:href="kg-20260630.xsd#kg_AmTrustQuotaShareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustQuotaShareMember" xlink:to="lab_kg_AmTrustQuotaShareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_019e18df-79c7-78cc-86d4-1e6d77c7fdd5_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, loan agreement, obligation threshold</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Loan Agreement, Obligation Threshold</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Loan Agreement, Obligation Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionLoanAgreementObligationThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:to="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FeeIncome_019e18df-79c7-7340-9fc7-4afef40769e9_terseLabel_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fee revenue</link:label>
    <link:label id="lab_us-gaap_FeeIncome_019e18df-79c7-7004-94dc-05702e32c363_verboseLabel_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fee revenue</link:label>
    <link:label id="lab_us-gaap_FeeIncome_label_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeeIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FeeIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FeeIncome" xlink:to="lab_us-gaap_FeeIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_019e18df-79c7-76e1-934c-2ba532fd549b_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Acquired [Line Items]</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Acquired [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_019e18df-7903-73f5-be7c-e35c76eb65dd_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock_019e18df-79c6-75c2-b819-fba57881c131_terseLabel_en-US" xlink:label="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Amortized Cost, Gross Unrealized Gains and Losses and Fair Value on Fixed Maturities</link:label>
    <link:label id="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock_label_en-US" xlink:label="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments Reconciliation [Table Text Block]</link:label>
    <link:label id="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock_documentation_en-US" xlink:label="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Investments Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:href="kg-20260630.xsd#kg_ScheduleOfInvestmentsReconciliationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:to="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019e18df-7903-709f-95b5-b1b552d0a1ee_verboseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019e18df-79c6-72fd-942e-fcd80459529d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember_019e18df-7a57-7630-bae6-cf64caab82d0_terseLabel_en-US" xlink:label="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
    <link:label id="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember_label_en-US" xlink:label="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockOwnershipHeldDirectlyMember_019e18df-79c7-723b-a1af-e801afcc52fa_terseLabel_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldDirectlyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock Held Directly</link:label>
    <link:label id="lab_kg_CommonStockOwnershipHeldDirectlyMember_label_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldDirectlyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Ownership, Held Directly [Member]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipHeldDirectlyMember_documentation_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldDirectlyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Ownership, Held Directly</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockOwnershipHeldDirectlyMember" xlink:href="kg-20260630.xsd#kg_CommonStockOwnershipHeldDirectlyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommonStockOwnershipHeldDirectlyMember" xlink:to="lab_kg_CommonStockOwnershipHeldDirectlyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019e18df-7a57-7ff7-ab00-55579c17aa94_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reporting segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount_019e18df-7a57-74c4-b4ea-8aecb0731917_negatedTerseLabel_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Discount for present value</link:label>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount_label_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Fair Value Discount</link:label>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount_documentation_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Fair Value Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:href="kg-20260630.xsd#kg_LesseeOperatingLeaseLiabilityFairValueDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:to="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019e18df-79c6-7995-9389-59e5ecadf49a_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember_019e18df-79c7-748c-965f-2e4940e2fe2e_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Value Change - Company Performance</link:label>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember_label_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Change in Guideline Public Company Multiples [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Change in Guideline Public Company Multiples</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:href="kg-20260630.xsd#kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:to="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_TerryLeeLedbetterMember_019e18df-7a57-784d-98f0-4ad9a57d8161_terseLabel_en-US" xlink:label="lab_kg_TerryLeeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Terry Lee Ledbetter</link:label>
    <link:label id="lab_kg_TerryLeeLedbetterMember_label_en-US" xlink:label="lab_kg_TerryLeeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Terry Lee Ledbetter [Member]</link:label>
    <link:label id="lab_kg_TerryLeeLedbetterMember_documentation_en-US" xlink:label="lab_kg_TerryLeeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Terry Lee Ledbetter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_TerryLeeLedbetterMember" xlink:href="kg-20260630.xsd#kg_TerryLeeLedbetterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_TerryLeeLedbetterMember" xlink:to="lab_kg_TerryLeeLedbetterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_019e18df-79c6-711c-98d1-d64024699f33_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, equity instruments other than options, grants in period (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionCancellationNoticePeriod_019e18df-7a57-7bcf-89a9-3e8c800db742_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cancellation notice period</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCancellationNoticePeriod_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Cancellation Notice Period</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCancellationNoticePeriod_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Cancellation Notice Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionCancellationNoticePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:to="lab_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_019e18df-7903-7dcc-a110-bbe114ad3b54_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SegmentConcentrationRiskMember_019e18df-7903-7e72-81c5-de7215e0809f_terseLabel_en-US" xlink:label="lab_kg_SegmentConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Concentration Risk</link:label>
    <link:label id="lab_kg_SegmentConcentrationRiskMember_label_en-US" xlink:label="lab_kg_SegmentConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Concentration Risk [Member]</link:label>
    <link:label id="lab_kg_SegmentConcentrationRiskMember_documentation_en-US" xlink:label="lab_kg_SegmentConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Segment Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SegmentConcentrationRiskMember" xlink:href="kg-20260630.xsd#kg_SegmentConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SegmentConcentrationRiskMember" xlink:to="lab_kg_SegmentConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019e18df-7902-727e-9dc3-e1413a975504_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelGroupMember_019e18df-7903-711f-ba0e-b9a53512ccbc_terseLabel_en-US" xlink:label="lab_kg_KestrelGroupMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group</link:label>
    <link:label id="lab_kg_KestrelGroupMember_label_en-US" xlink:label="lab_kg_KestrelGroupMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Group [Member]</link:label>
    <link:label id="lab_kg_KestrelGroupMember_documentation_en-US" xlink:label="lab_kg_KestrelGroupMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Group</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupMember" xlink:href="kg-20260630.xsd#kg_KestrelGroupMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelGroupMember" xlink:to="lab_kg_KestrelGroupMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_country_US_019e18df-79c6-70df-8a30-f53b52894b95_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
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    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019e18df-79c7-7e5a-a8a2-a74d498f0d3c_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
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    <link:label id="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_019e18df-7903-7c0b-8cfe-f99a8bf5867f_terseLabel_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss) income before reclassifications</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent"/>
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    <link:label id="lab_kg_BusinessCombinationStockConversionRatio_019e18df-7902-7e77-9ea6-29ca323bcccd_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationStockConversionRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combination, stock conversion ratio</link:label>
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    <link:label id="lab_kg_BusinessCombinationStockConversionRatio_documentation_en-US" xlink:label="lab_kg_BusinessCombinationStockConversionRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Stock Conversion Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationStockConversionRatio" xlink:href="kg-20260630.xsd#kg_BusinessCombinationStockConversionRatio"/>
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    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease_019e18df-79c7-7de3-870d-ddfab22048da_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of ceding commission payable, period increase</link:label>
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    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Of Ceding Commission Payable, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease"/>
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    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019e18df-79c7-750d-9fdd-01aa38dba3c4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Reportable Segments Underwriting Results to Consolidated Net Loss</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract_019e18df-79c6-7851-a9a4-c0012c296a8c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss) income</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019e18df-79c7-7a1b-b4a3-d46a6484d039_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesGross_019fa235-d027-7e24-ad50-084004238fe6_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance receivable</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverablesGross"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019e18df-79c7-731c-8c92-e32237fba4fc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net current period other comprehensive income (loss)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
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    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome_019e18df-7a58-716d-bd62-73b2f63460be_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued investment income</link:label>
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    <link:label id="lab_kg_AmtrustFinancialServicesIncMember_019e18df-7903-7fbf-a6f7-c421bdcf20f7_terseLabel_en-US" xlink:label="lab_kg_AmtrustFinancialServicesIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Financial Services, Inc.</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff_019e18df-79c7-778f-9a08-f4c07fc57a75_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Allowance for Credit Loss, Writeoff</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_019e18df-79c6-7616-bfe1-38c52cc72f6c_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scheduled of Maturity of Operating Lease Liabilities</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019e18df-79c7-75d5-891a-1599341cf1b8_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVenture2Member_019e18df-79c7-7b37-b94c-1f0defa25c5c_terseLabel_en-US" xlink:label="lab_kg_SilverstoneVenture2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Silverstone Venture 2</link:label>
    <link:label id="lab_kg_SilverstoneVenture2Member_label_en-US" xlink:label="lab_kg_SilverstoneVenture2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Silverstone Venture 2 [Member]</link:label>
    <link:label id="lab_kg_SilverstoneVenture2Member_documentation_en-US" xlink:label="lab_kg_SilverstoneVenture2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Silverstone Venture 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVenture2Member" xlink:href="kg-20260630.xsd#kg_SilverstoneVenture2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SilverstoneVenture2Member" xlink:to="lab_kg_SilverstoneVenture2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019e18df-7903-7d04-8609-4d17be0f348c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross_019e18df-7903-7cb2-b3ad-616b9ffcc98f_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverables on unpaid losses</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables on Unpaid Losses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross" xlink:to="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019e18df-79c7-71b0-a016-3891164088da_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockOwnershipHeldIndirectlyMember_019e18df-79c6-746d-9392-3a7f5c909789_terseLabel_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock Held Indirectly</link:label>
    <link:label id="lab_kg_CommonStockOwnershipHeldIndirectlyMember_label_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Ownership, Held Indirectly [Member]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipHeldIndirectlyMember_documentation_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Ownership, Held Indirectly</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:href="kg-20260630.xsd#kg_CommonStockOwnershipHeldIndirectlyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:to="lab_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_019e18df-7a58-77cc-b891-298d0472572a_terseLabel_en-US" xlink:label="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of securities in an unrealized loss position</link:label>
    <link:label id="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_label_en-US" xlink:label="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Securities in Unrealized Loss Positions, Qualitative Disclosure, Number of Positions</link:label>
    <link:label id="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_documentation_en-US" xlink:label="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Securities in Unrealized Loss Positions, Qualitative Disclosure, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:href="kg-20260630.xsd#kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:to="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_019e18df-79c6-778d-b7b9-6720cd1f3ca5_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, gross losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_019e18df-79c7-77e0-b527-7d02b1a05c9d_negatedLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Treasury shares, at cost (2026: 2,284,570 shares, 2025: 2,237,534 shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonValue" xlink:to="lab_us-gaap_TreasuryStockCommonValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_019e18df-7a57-711f-81db-bfb02a3c9f40_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingActivityByTypeDomain_019fb8af-788f-7e69-b966-f07bf054ff1e_terseLabel_en-US" xlink:label="lab_us-gaap_TradingActivityByTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Activity, by Type [Domain]</link:label>
    <link:label id="lab_us-gaap_TradingActivityByTypeDomain_label_en-US" xlink:label="lab_us-gaap_TradingActivityByTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Activity, by Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingActivityByTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TradingActivityByTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingActivityByTypeDomain" xlink:to="lab_us-gaap_TradingActivityByTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember_019e18df-79c7-72bb-aafe-276bbaddf08a_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBITDA &amp; Commission Equity Volatility Rate</link:label>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember_label_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA and Commission Volatility Rate [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA and Commission Volatility Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:href="kg-20260630.xsd#kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:to="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_019e18df-7a58-7796-b80d-1a059def2787_terseLabel_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of unrealized loss positions</link:label>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_label_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Continuous Unrealized Loss Position, Fair Value</link:label>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_documentation_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Continuous Unrealized Loss Position, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:href="kg-20260630.xsd#kg_InvestmentsContinuousUnrealizedLossPositionFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:to="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet_019e18df-7a57-75db-bb92-0cf0e9e3dec2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss and LAE ceded</link:label>
    <link:label id="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet_label_en-US" xlink:label="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Assumed and Ceded</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceCostsAndRecoveriesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:to="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019e18df-79c7-722b-821e-7e97cf751f27_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive (loss) income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019e18df-7a57-75a7-982d-be38b2e7ff6c_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_019e18df-79c7-70a1-afff-ba820a6933a7_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019e18df-7a57-7db3-ad1c-bb9bfc4081ed_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per Common Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019e18df-79c7-7685-a99f-ddeb7393b41f_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019e18df-79c7-7b79-95f2-4973fb9e0475_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock_019e18df-7902-7172-b8cb-3c43571317a0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Premiums by Major Line of Business</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Product and Service, Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:to="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019e18df-7a57-72d9-b58d-f9636923743c_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019e18df-79c7-70c2-b547-cae0572de01c_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019e18df-7a58-7c3c-8a83-9c1c8b5c288b_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_019e18df-79c7-77b7-a487-dc2064eb3f39_terseLabel_en-US" xlink:label="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diversified Reinsurance Segment</link:label>
    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_019e18df-79c7-7941-809c-1afb0fa5358f_verboseLabel_en-US" xlink:label="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diversified Reinsurance legacy business</link:label>
    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Diversified Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Diversified Reinsurance Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiversifiedReinsuranceSegmentMember" xlink:href="kg-20260630.xsd#kg_DiversifiedReinsuranceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DiversifiedReinsuranceSegmentMember" xlink:to="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_019e18df-79c6-7ef8-a9fb-31ec37b8810a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Purchase Price of Assets and Liabilities Assumed</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired and Liability Assumed [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_019e18df-7a57-74d8-bedb-b2e84290b070_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized losses during the period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Other Comprehensive Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_019e18df-79c7-799a-bf78-a14890d401c3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amounts reclassified from AOCI to net loss, net of tax</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from AOCI, Current Period, before Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent"/>
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    <link:label id="lab_kg_GLSToRPPMember_019e18df-79c7-7e24-b834-2e2b7dbb2359_terseLabel_en-US" xlink:label="lab_kg_GLSToRPPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GLS to RPP</link:label>
    <link:label id="lab_kg_GLSToRPPMember_label_en-US" xlink:label="lab_kg_GLSToRPPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GLS to RPP [Member]</link:label>
    <link:label id="lab_kg_GLSToRPPMember_documentation_en-US" xlink:label="lab_kg_GLSToRPPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GLS to RPP</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GLSToRPPMember" xlink:href="kg-20260630.xsd#kg_GLSToRPPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GLSToRPPMember" xlink:to="lab_kg_GLSToRPPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_019e18df-7903-7605-b6a1-fd7397990c4d_terseLabel_en-US" xlink:label="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments transferred out related to Partial Termination Amendment and Commutation</link:label>
    <link:label id="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_label_en-US" xlink:label="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Quota Shares Reinsurance Agreement, Partial Termination Amendment [Member]</link:label>
    <link:label id="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_documentation_en-US" xlink:label="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Quota Shares Reinsurance Agreement, Partial Termination Amendment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:href="kg-20260630.xsd#kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:to="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCost_019e18df-79c6-74cc-9bf1-89ebf6693abe_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity securities, at fair value, cost</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCost_019e18df-79c6-7bf8-8287-61946f68a77a_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCost_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiCost" xlink:to="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019e18df-79c7-7ab1-a829-51219a63d97a_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and loss adjustment expenses (includes $478,831 and $554,507 from related parties in 2026 and 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019e18df-79c7-747a-8941-1aed711424c3_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and loss adjustment expenses</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019e18df-79c7-7a08-b77b-9bf05978fc2e_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and LAE</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019e18df-79c7-7b37-895d-3fba226e6d9f_periodStartLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Gross loss and LAE reserves, January 1</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019e18df-79c7-784e-9b70-ed955ee33941_periodEndLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Gross loss and LAE reserves, June 30</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Claims and Claims Adjustment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:to="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019e18df-79c7-7501-86f8-a339dcb4434f_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_019e18df-79c7-7720-9caf-5959ca1832a0_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares issued or to be issued (in shares)</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_label_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Shares issued or To Be Issued</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_documentation_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Shares issued or To Be Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:href="kg-20260630.xsd#kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued"/>
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    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_019e18df-79c7-7875-9527-42a51eaf7682_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_019e18df-79c7-7812-ae9c-31266fa0b429_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet"/>
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    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_019e18df-7a57-7183-95ad-625b694c3207_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Investment Income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeTextBlock" xlink:to="lab_us-gaap_InvestmentIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_019e18df-7903-7406-a94c-ea22d30120ef_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. treasury bills</link:label>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasurySecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_USTreasurySecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasurySecuritiesMember" xlink:to="lab_us-gaap_USTreasurySecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLossCarryforwards_019e18df-79c7-72ea-bc73-9a7be11c1234_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwards" xlink:to="lab_us-gaap_OperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TypeOfArrangementAxis_019e18df-7a57-7f2f-918c-043fd97154dc_terseLabel_en-US" xlink:label="lab_us-gaap_TypeOfArrangementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
    <link:label id="lab_us-gaap_TypeOfArrangementAxis_label_en-US" xlink:label="lab_us-gaap_TypeOfArrangementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TypeOfArrangementAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TypeOfArrangementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TypeOfArrangementAxis" xlink:to="lab_us-gaap_TypeOfArrangementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable_019e18df-79c7-7e19-a520-cb450f194d27_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Intangible Asset, Acquired, Finite-Lived [Table]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Intangible Asset, Acquired, Finite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable"/>
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    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_019e18df-7902-70cf-a2eb-c30eb0a0c8f0_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Potentially dilutive securities (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted, Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment"/>
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    <link:label id="lab_us-gaap_OtherGeneralAndAdministrativeExpense_019e18df-7903-72d4-962a-29862d7b1326_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other general and administrative expenses</link:label>
    <link:label id="lab_us-gaap_OtherGeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherGeneralAndAdministrativeExpense"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019e18df-79c7-7758-8de4-7fe3cfba7369_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Other Investments Measured at Fair value on a Recurring Basis Using Level 3 Inputs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
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    <link:label id="lab_kg_InvestmentManagementFeesMember_019e18df-79c7-7a22-a28b-0824bb3cb103_terseLabel_en-US" xlink:label="lab_kg_InvestmentManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Management Fee</link:label>
    <link:label id="lab_kg_InvestmentManagementFeesMember_label_en-US" xlink:label="lab_kg_InvestmentManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Management Fees [Member]</link:label>
    <link:label id="lab_kg_InvestmentManagementFeesMember_documentation_en-US" xlink:label="lab_kg_InvestmentManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Management Fees [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentManagementFeesMember" xlink:href="kg-20260630.xsd#kg_InvestmentManagementFeesMember"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_019e18df-7a57-79b5-a770-7ffaf653175b_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost of securities without single maturities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, without Single Maturity Date, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost"/>
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    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionSolvencyRatio_019e18df-7903-7c3d-8c8e-4d59f80a60b9_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionSolvencyRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Solvency ratio</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionSolvencyRatio_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionSolvencyRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Solvency Ratio</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionSolvencyRatio_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionSolvencyRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Solvency Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionSolvencyRatio" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionSolvencyRatio"/>
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    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
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    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019e18df-7a57-75aa-b545-5f381c29ca25_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss and loss adjustment expenses</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019e18df-7a57-755c-9d24-8fd2d352014c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net loss and LAE</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019e18df-7a57-7367-aa1e-0192dd171d49_totalLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019e18df-7a57-706f-8f97-e6a7c38d1963_negatedLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net loss and LAE</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:to="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019e18df-79c7-77bf-9bd6-a64398dd49f1_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Quoted Prices in Active Markets for Identical Assets (Level 1)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet_019e18df-7a57-7883-abc3-a156631dbfba_periodStartLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Net loss and LAE reserves, January 1</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet_019e18df-7a57-7ed0-8420-29f8bafdc5e0_periodEndLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Net loss and LAE reserves, June 30</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:to="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_019e18df-7903-75a6-b14d-62f5f5869f9f_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral held by related party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Collateral Held by Related Party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Collateral Held by Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionCollateralHeldByRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:to="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NumberOfDirectorsSelectedByAffiliate_019e18df-7903-7934-8d39-dcb5b48c2231_terseLabel_en-US" xlink:label="lab_kg_NumberOfDirectorsSelectedByAffiliate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of directors, selected by affiliate</link:label>
    <link:label id="lab_kg_NumberOfDirectorsSelectedByAffiliate_label_en-US" xlink:label="lab_kg_NumberOfDirectorsSelectedByAffiliate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Directors, Selected by Affiliate</link:label>
    <link:label id="lab_kg_NumberOfDirectorsSelectedByAffiliate_documentation_en-US" xlink:label="lab_kg_NumberOfDirectorsSelectedByAffiliate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Directors, Selected by Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfDirectorsSelectedByAffiliate" xlink:href="kg-20260630.xsd#kg_NumberOfDirectorsSelectedByAffiliate"/>
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    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_019e18df-7a57-7635-b765-636a36af2281_negatedLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Senior notes - at fair value</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Long-Term Debt</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure_019e18df-7902-7b07-98ba-9d9bed459b48_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral on exposure</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percentage Of Collateral On Exposure</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percentage Of Collateral On Exposure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPercentageOfCollateralOnExposure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:to="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_019e18df-79c7-7470-9c80-f690e5b76853_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount_019e18df-79c6-7b9f-80c0-175915fbbaf7_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for losses incurred but not reported ("IBNR")</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Incurred but Not Reported (IBNR) Claims, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount"/>
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    <link:label id="lab_kg_PremiumsWrittenNetAsPercentOfTotal_019e18df-79c7-75f7-af7a-cf5c062d26c5_terseLabel_en-US" xlink:label="lab_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of total net premiums written</link:label>
    <link:label id="lab_kg_PremiumsWrittenNetAsPercentOfTotal_label_en-US" xlink:label="lab_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Net as a Percent of Total</link:label>
    <link:label id="lab_kg_PremiumsWrittenNetAsPercentOfTotal_documentation_en-US" xlink:label="lab_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premiums Written, Net as a Percent of Total</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:href="kg-20260630.xsd#kg_PremiumsWrittenNetAsPercentOfTotal"/>
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    <link:label id="lab_us-gaap_PlanNameDomain_019e18df-7902-7469-9bda-530b4b9ad6cb_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:label id="lab_us-gaap_PlanNameDomain_label_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameDomain" xlink:to="lab_us-gaap_PlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_019e18df-79c7-7f19-928c-dab660951cc4_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total securities with single maturities, amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis"/>
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    <link:label id="lab_srt_ScenarioUnspecifiedDomain_019e18df-7a57-7a1e-b533-ee96cf8516ed_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioUnspecifiedDomain" xlink:to="lab_srt_ScenarioUnspecifiedDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019e18df-7903-783e-b91e-46444d490a35_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, right-of-use asset</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
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    <link:label id="lab_us-gaap_OperatingLossCarryforwardsLineItems_019e18df-79c7-7ac0-be5d-e4ad6294ca68_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Line Items]</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsLineItems_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLossCarryforwardsLineItems"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
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    <link:label id="lab_kg_BusinessCombinationProvisionalInformationInitialAccountingIncompleteGainLossOnAdjustment_019fd790-cbb2-7196-a25d-f87a4cc2faa3_negatedTerseLabel_en-US" xlink:label="lab_kg_BusinessCombinationProvisionalInformationInitialAccountingIncompleteGainLossOnAdjustment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Decrease in fair value of net acquired assets</link:label>
    <link:label id="lab_kg_BusinessCombinationProvisionalInformationInitialAccountingIncompleteGainLossOnAdjustment_label_en-US" xlink:label="lab_kg_BusinessCombinationProvisionalInformationInitialAccountingIncompleteGainLossOnAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Gain (Loss) on Adjustment</link:label>
    <link:label id="lab_kg_BusinessCombinationProvisionalInformationInitialAccountingIncompleteGainLossOnAdjustment_documentation_en-US" xlink:label="lab_kg_BusinessCombinationProvisionalInformationInitialAccountingIncompleteGainLossOnAdjustment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Gain (Loss) on Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationProvisionalInformationInitialAccountingIncompleteGainLossOnAdjustment" xlink:href="kg-20260630.xsd#kg_BusinessCombinationProvisionalInformationInitialAccountingIncompleteGainLossOnAdjustment"/>
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    <link:label id="lab_kg_BusinessCombinationAcquisitionOptionTerm_019e18df-79c6-716d-86f0-cb0570d2dfd9_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition option term</link:label>
    <link:label id="lab_kg_BusinessCombinationAcquisitionOptionTerm_label_en-US" xlink:label="lab_kg_BusinessCombinationAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Option Term</link:label>
    <link:label id="lab_kg_BusinessCombinationAcquisitionOptionTerm_documentation_en-US" xlink:label="lab_kg_BusinessCombinationAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Option Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationAcquisitionOptionTerm" xlink:href="kg-20260630.xsd#kg_BusinessCombinationAcquisitionOptionTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationAcquisitionOptionTerm" xlink:to="lab_kg_BusinessCombinationAcquisitionOptionTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_OtherInvestmentMember_019e18df-7a58-7bb1-b72e-5173cd3f9b5e_terseLabel_en-US" xlink:label="lab_kg_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_kg_OtherInvestmentMember_label_en-US" xlink:label="lab_kg_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investment [Member]</link:label>
    <link:label id="lab_kg_OtherInvestmentMember_documentation_en-US" xlink:label="lab_kg_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentMember" xlink:href="kg-20260630.xsd#kg_OtherInvestmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OtherInvestmentMember" xlink:to="lab_kg_OtherInvestmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_019e18df-7903-7306-a26f-f0657b3b883f_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_019e18df-7903-78aa-83ca-25f68bd9aad4_verboseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss_019e18df-7a57-7928-bf43-02985b3180ee_negatedTerseLabel_en-US" xlink:label="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Equity securities, gross losses</link:label>
    <link:label id="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss_label_en-US" xlink:label="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized And Unrealized Loss</link:label>
    <link:label id="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss_documentation_en-US" xlink:label="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized And Unrealized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss" xlink:href="kg-20260630.xsd#kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss" xlink:to="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember_019e18df-7a57-7d6b-a5ec-539c0c35e893_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Market comparable companies &amp; Option Pricing Models</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Price of Comparable Business [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember" xlink:to="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementScenarioAxis_019e18df-79c6-72c0-a041-f31d3218d06b_terseLabel_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementScenarioAxis" xlink:to="lab_srt_StatementScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019e18df-7903-7d30-b14b-7eed5a6ec26b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: unamortized fair value adjustment</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments_019e18df-7902-77fa-836a-572078c4c064_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Other Investments</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_019e18df-79c7-7974-958a-f113682df6c8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_019e18df-79c6-76d3-b51c-da413887170e_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loan receivable from related party</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Net Loan Receivable From Related Party</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Net Loan Receivable From Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_019e18df-7903-794c-9f3c-fbfcdd1aa349_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_019e18df-7a57-74eb-b053-d1f6691ddb25_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, available-for-sale, at fair value</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Fixed Maturities, Available For Sale</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Fixed Maturities, Available For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_019e18df-79c7-77e2-98dd-a64a2a7c51d5_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_019e18df-79c7-7d2b-9da2-ee4a2922ccc1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of equity method investments</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019e18df-7a58-716f-b7a5-07511f86a79f_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stated interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019e18df-7a58-7ed2-b0f0-ff8c7f83dd19_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Coupon rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_019e18df-7903-72ac-b37a-db00abd76cb5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distribution to shareholders</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_019e18df-79c7-7093-934b-6680ebd441ff_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net, allowance for expected credit losses</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_label_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:to="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019e18df-7903-7428-b7b5-c84e739a6cb5_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total shareholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019e18df-7903-7f37-9138-dd65113b6002_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019e18df-7903-76b3-bab8-56316a29bc1a_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeAxis_019e18df-7903-7fcd-8abc-e328d7edc178_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Axis]</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeAxis_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Axis]</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeAxis_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionByTypeAxis" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionByTypeAxis" xlink:to="lab_kg_RelatedPartyTransactionByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019e18df-7903-71ed-9f8e-194ac6152127_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019e18df-7902-7c17-8aff-954b74be13e3_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019e18df-7902-728f-8043-d061e26747b5_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group Ltd shares issued at Closing (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest, Share Issued, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherInvestments_019e18df-79c6-7639-8757-b3570aedeb9d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_us-gaap_OtherInvestments_019e18df-79c6-72b1-91fc-fa59cb2ebc09_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total other investments at fair value</link:label>
    <link:label id="lab_us-gaap_OtherInvestments_label_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInvestments" xlink:to="lab_us-gaap_OtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_019e18df-79c7-7a65-a7be-26c38fa0cff9_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, available-for-sale, at fair value, amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_019e18df-79c7-7fe5-84cf-10ed4b65cfc7_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Original or amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_019e18df-79c7-78e3-9b5c-07adc1317c0d_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion of the Maiden awards attributable to pre-combination service</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_label_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Consideration Transferred Attributable to Pre Combination Service</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Consideration Transferred Attributable to Pre Combination Service</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:href="kg-20260630.xsd#kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:to="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PerformanceSharesMember_019fa214-9ba7-7d9b-b1f3-cfb7f75b3e9f_terseLabel_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Shares</link:label>
    <link:label id="lab_us-gaap_PerformanceSharesMember_label_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Shares [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PerformanceSharesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PerformanceSharesMember" xlink:to="lab_us-gaap_PerformanceSharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RealizedAndUnrealizedGainOnInvestments_019e18df-79c7-71bd-880c-2d6ecac0e564_totalLabel_en-US" xlink:label="lab_kg_RealizedAndUnrealizedGainOnInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized gains (losses) on investment, gross gains</link:label>
    <link:label id="lab_kg_RealizedAndUnrealizedGainOnInvestments_label_en-US" xlink:label="lab_kg_RealizedAndUnrealizedGainOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized And Unrealized Gain On Investments</link:label>
    <link:label id="lab_kg_RealizedAndUnrealizedGainOnInvestments_documentation_en-US" xlink:label="lab_kg_RealizedAndUnrealizedGainOnInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Realized And Unrealized Gain On Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealizedAndUnrealizedGainOnInvestments" xlink:href="kg-20260630.xsd#kg_RealizedAndUnrealizedGainOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RealizedAndUnrealizedGainOnInvestments" xlink:to="lab_kg_RealizedAndUnrealizedGainOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_QuotaShareReinsuranceAgreementsMember_019e18df-7902-7bcd-9713-9cd0e9c456cc_terseLabel_en-US" xlink:label="lab_kg_QuotaShareReinsuranceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quota Share Reinsurance Agreements</link:label>
    <link:label id="lab_kg_QuotaShareReinsuranceAgreementsMember_label_en-US" xlink:label="lab_kg_QuotaShareReinsuranceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Quota Share Reinsurance Agreements [Member]</link:label>
    <link:label id="lab_kg_QuotaShareReinsuranceAgreementsMember_documentation_en-US" xlink:label="lab_kg_QuotaShareReinsuranceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Quota Share Reinsurance Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_QuotaShareReinsuranceAgreementsMember" xlink:href="kg-20260630.xsd#kg_QuotaShareReinsuranceAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_QuotaShareReinsuranceAgreementsMember" xlink:to="lab_kg_QuotaShareReinsuranceAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019e18df-79c7-7cab-9123-a612ded6a023_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff_019e18df-7a57-79aa-8fc3-e4392f2eea79_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Write off on the accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAccruedInterestWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:to="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_019e18df-7a57-7009-ae15-e90e5a983c27_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipAxis" xlink:to="lab_srt_OwnershipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019e18df-7a57-73ae-92bd-f7692871cb52_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_019e18df-79c7-745d-9e2b-f23794ad66d0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DirectLendingEntitiesMember_019e18df-7902-7d33-9338-16b743cca4de_terseLabel_en-US" xlink:label="lab_kg_DirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments in direct lending entities</link:label>
    <link:label id="lab_kg_DirectLendingEntitiesMember_label_en-US" xlink:label="lab_kg_DirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Lending Entities [Member]</link:label>
    <link:label id="lab_kg_DirectLendingEntitiesMember_documentation_en-US" xlink:label="lab_kg_DirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Direct Lending Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DirectLendingEntitiesMember" xlink:href="kg-20260630.xsd#kg_DirectLendingEntitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DirectLendingEntitiesMember" xlink:to="lab_kg_DirectLendingEntitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019e18df-7903-7602-8108-c2efdfed32ec_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FixedMaturitiesMember_019e18df-79c7-7d64-8200-d4e986a38ab6_verboseLabel_en-US" xlink:label="lab_us-gaap_FixedMaturitiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities</link:label>
    <link:label id="lab_us-gaap_FixedMaturitiesMember_label_en-US" xlink:label="lab_us-gaap_FixedMaturitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FixedMaturitiesMember" xlink:to="lab_us-gaap_FixedMaturitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentHoldingsTextBlock_019e18df-7903-7a1d-89a1-2ffaf82d4069_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentHoldingsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_InvestmentHoldingsTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentHoldingsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Holdings [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentHoldingsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentHoldingsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentHoldingsTextBlock" xlink:to="lab_us-gaap_InvestmentHoldingsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceTableTextBlock_019e18df-79c7-7039-b243-b3e2853651f8_terseLabel_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Effect of Ceded Reinsurance on Net Premiums Written and Earned and on Net Loss and LAE</link:label>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceTableTextBlock_label_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effects of Reinsurance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectsOfReinsuranceTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:to="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019e18df-7a58-759c-8dfe-2314b50f39aa_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fed funds rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_019e18df-7903-7f4c-8546-0c6a36b68585_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Other Asset, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther"/>
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    <link:label id="lab_us-gaap_RestrictedStockMember_019e18df-79c7-77d6-b8ca-c2e6f003727d_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019e18df-7a57-7ee3-91ec-4ed2cfd2df5f_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive (loss) income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019e18df-7a57-735f-bee9-48fdc9370e61_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019e18df-7903-73c9-8808-39117fc4feb2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_019e18df-79c6-775b-93e8-85dc770eca46_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net equity portion of consideration transferred at Closing</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable"/>
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    <link:label id="lab_kg_CavelloMember_019e18df-79c7-7ddd-9828-66bf456fd545_terseLabel_en-US" xlink:label="lab_kg_CavelloMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cavello</link:label>
    <link:label id="lab_kg_CavelloMember_label_en-US" xlink:label="lab_kg_CavelloMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cavello [Member]</link:label>
    <link:label id="lab_kg_CavelloMember_documentation_en-US" xlink:label="lab_kg_CavelloMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cavello</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CavelloMember" xlink:href="kg-20260630.xsd#kg_CavelloMember"/>
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    <link:label id="lab_us-gaap_StatementLineItems_019e18df-7903-7f01-9806-44c5d83fdff7_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019e18df-7903-7856-b5a3-7d45331a8470_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuableTreasurySharesRetained" xlink:href="kg-20260630.xsd#kg_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuableTreasurySharesRetained"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuableTreasurySharesRetained" xlink:to="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuableTreasurySharesRetained" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrivateEquityFundsMember_019e18df-79c7-7ca6-bdeb-cb9d420ed409_terseLabel_en-US" xlink:label="lab_us-gaap_PrivateEquityFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity funds</link:label>
    <link:label id="lab_us-gaap_PrivateEquityFundsMember_label_en-US" xlink:label="lab_us-gaap_PrivateEquityFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Equity Funds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivateEquityFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrivateEquityFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrivateEquityFundsMember" xlink:to="lab_us-gaap_PrivateEquityFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_019e18df-79c7-76ff-9e54-a7ab0b9564b1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net gains recognized for equity securities divested</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:to="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeNet_019e18df-79c7-7f7e-8cd4-da7af6114121_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeNet_019e18df-79c7-7fa9-b65c-71f761a8768d_totalLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net investment income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeNet_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeNet" xlink:to="lab_us-gaap_InvestmentIncomeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_019e18df-7a57-7a59-b4f6-7aed3a99f11d_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FairValueInitialAssessmentMember_019fd799-a6dd-7f3f-a69b-b37d06a8802c_terseLabel_en-US" xlink:label="lab_kg_FairValueInitialAssessmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial Assessment</link:label>
    <link:label id="lab_kg_FairValueInitialAssessmentMember_label_en-US" xlink:label="lab_kg_FairValueInitialAssessmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Initial Assessment [Member]</link:label>
    <link:label id="lab_kg_FairValueInitialAssessmentMember_documentation_en-US" xlink:label="lab_kg_FairValueInitialAssessmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Initial Assessment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FairValueInitialAssessmentMember" xlink:href="kg-20260630.xsd#kg_FairValueInitialAssessmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FairValueInitialAssessmentMember" xlink:to="lab_kg_FairValueInitialAssessmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax_019e18df-7903-723b-974b-d364650e7090_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Adjustment for reclassification of net realized losses recognized in net loss</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Reclassification Adjustment from AOCI for Sale of Securities, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_019e18df-79c7-7ef6-ac69-2c1f76607c5c_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross unrealized gains</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVenture1Member_019e18df-79c7-7768-b0bf-c8658d31bc09_terseLabel_en-US" xlink:label="lab_kg_SilverstoneVenture1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Silverstone Venture 1</link:label>
    <link:label id="lab_kg_SilverstoneVenture1Member_label_en-US" xlink:label="lab_kg_SilverstoneVenture1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Silverstone Venture 1 [Member]</link:label>
    <link:label id="lab_kg_SilverstoneVenture1Member_documentation_en-US" xlink:label="lab_kg_SilverstoneVenture1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Silverstone Venture 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVenture1Member" xlink:href="kg-20260630.xsd#kg_SilverstoneVenture1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SilverstoneVenture1Member" xlink:to="lab_kg_SilverstoneVenture1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_019e18df-7902-7f08-a875-53d42574e070_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value of securities without single maturities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, without Single Maturity Date, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_019e18df-79c7-7ba5-8979-f4a177bdc2b0_terseLabel_en-US" xlink:label="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards, with no expiry date, percentage</link:label>
    <link:label id="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_label_en-US" xlink:label="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration, Percentage</link:label>
    <link:label id="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_documentation_en-US" xlink:label="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:href="kg-20260630.xsd#kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:to="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededCreditRiskReinsurerDomain_019e18df-7a57-7b0f-a856-c37975852fb8_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskReinsurerDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_CededCreditRiskReinsurerDomain_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskReinsurerDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain" xlink:to="lab_us-gaap_CededCreditRiskReinsurerDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment_019e18df-7903-746d-8178-83f6793ebb9e_negatedTerseLabel_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Effect of foreign exchange rate movements</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment_label_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Foreign Currency Transaction and Translation Adjustment</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment_documentation_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (decrease) in liability for unpaid claims and claims adjustment expense due to foreign currency transaction and translation adjustments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:href="kg-20260630.xsd#kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:to="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FixedIncomeSecuritiesMember_019e18df-7903-7df1-84e0-44a0d1702514_terseLabel_en-US" xlink:label="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities</link:label>
    <link:label id="lab_us-gaap_FixedIncomeSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Income Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedIncomeSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FixedIncomeSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FixedIncomeSecuritiesMember" xlink:to="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities_019e18df-7a57-7806-94af-523b8f95455d_totalLabel_en-US" xlink:label="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other investments, net</link:label>
    <link:label id="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities_label_en-US" xlink:label="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Other Securities, Excluding Debt and Equity Securities</link:label>
    <link:label id="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities_documentation_en-US" xlink:label="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Other Securities, Excluding Debt and Equity Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:href="kg-20260630.xsd#kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities"/>
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    <link:label id="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock_019e18df-7a57-72dc-8557-1be19d31c586_terseLabel_en-US" xlink:label="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of the Credit Ratings of Fixed Maturities</link:label>
    <link:label id="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock_label_en-US" xlink:label="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investment Credit Ratings [Table Text Block]</link:label>
    <link:label id="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock_documentation_en-US" xlink:label="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Investment Credit Ratings [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable_019e18df-7903-7fae-a1be-ff4154c5fe07_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accrued investment income</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Investment Income Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_019e18df-7a58-7a1f-b1d2-4b3100b85df9_negatedLabel_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Total PPD for Legacy Reinsurance Segment</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_019e18df-7a58-7dc3-907d-db9211f877f4_terseLabel_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total AmTrust Reinsurance PPD</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_019e18df-7a58-7a7f-b0d3-d74f92b15bb2_negatedTerseLabel_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Total AmTrust Reinsurance PPD</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_label_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Period Increase (Decrease), Net of Commission Changes</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_documentation_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Period Increase (Decrease), Net of Commission Changes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:href="kg-20260630.xsd#kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:to="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiGainLoss_019e18df-79c7-75b2-ad34-31f24a5d8c9a_totalLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Equity securities, net</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiGainLoss_019e18df-79c7-7141-a26c-123a969d1dfd_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gains recognized for equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiGainLoss_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:to="lab_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsNetUnrealizedGainLoss_019e18df-7902-7b0c-8434-70af1bce6dfc_terseLabel_en-US" xlink:label="lab_kg_InvestmentsNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains on fixed maturity investments</link:label>
    <link:label id="lab_kg_InvestmentsNetUnrealizedGainLoss_label_en-US" xlink:label="lab_kg_InvestmentsNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Net Unrealized Gain (Loss)</link:label>
    <link:label id="lab_kg_InvestmentsNetUnrealizedGainLoss_documentation_en-US" xlink:label="lab_kg_InvestmentsNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Net Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsNetUnrealizedGainLoss" xlink:href="kg-20260630.xsd#kg_InvestmentsNetUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsNetUnrealizedGainLoss" xlink:to="lab_kg_InvestmentsNetUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019e18df-7903-7f56-a268-5f5f4f4c4299_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_019e18df-7903-7180-a1ed-b6c1598c01e6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019e18df-79c7-7df2-809c-4fd00dcdc927_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019e18df-79c7-712c-92ca-1f044cfa0365_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_019e18df-7903-76af-a202-186002b8bf43_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation</link:label>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Foreign Currency Adjustment Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedTranslationAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:to="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GenesisLegacySolutionsMember_019e18df-7903-77ef-93f0-425f0527159c_terseLabel_en-US" xlink:label="lab_kg_GenesisLegacySolutionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Genesis Legacy Solutions</link:label>
    <link:label id="lab_kg_GenesisLegacySolutionsMember_label_en-US" xlink:label="lab_kg_GenesisLegacySolutionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Genesis Legacy Solutions [Member]</link:label>
    <link:label id="lab_kg_GenesisLegacySolutionsMember_documentation_en-US" xlink:label="lab_kg_GenesisLegacySolutionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Genesis Legacy Solutions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GenesisLegacySolutionsMember" xlink:href="kg-20260630.xsd#kg_GenesisLegacySolutionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GenesisLegacySolutionsMember" xlink:to="lab_kg_GenesisLegacySolutionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_019e18df-79c7-777b-955d-0e7c7418295f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Carrying Value and Fair Value of Senior Notes</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019e18df-79c7-763e-9dca-890fb63b9487_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (loss) earnings per share attributable to Kestrel shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_LitigationCaseTypeDomain_019e18df-7902-78d0-8ec0-edd292da2638_terseLabel_en-US" xlink:label="lab_srt_LitigationCaseTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Case [Domain]</link:label>
    <link:label id="lab_srt_LitigationCaseTypeDomain_label_en-US" xlink:label="lab_srt_LitigationCaseTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Case [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_LitigationCaseTypeDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_LitigationCaseTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_LitigationCaseTypeDomain" xlink:to="lab_srt_LitigationCaseTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_019e18df-7903-7ba2-be49-95bbc0a09520_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of intangible assets</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
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    <link:label id="lab_kg_RestrictedCashAndInvestmentsLineItems_019e18df-7a57-7498-8f99-21c7554020f4_terseLabel_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments Items [Line Items]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsLineItems_label_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments [Line Items]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsLineItems_documentation_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsLineItems" xlink:href="kg-20260630.xsd#kg_RestrictedCashAndInvestmentsLineItems"/>
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    <link:label id="lab_kg_NumberOfDirectors_019e18df-79c6-777b-8a63-3720e7e736d4_terseLabel_en-US" xlink:label="lab_kg_NumberOfDirectors" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of directors</link:label>
    <link:label id="lab_kg_NumberOfDirectors_label_en-US" xlink:label="lab_kg_NumberOfDirectors" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Directors</link:label>
    <link:label id="lab_kg_NumberOfDirectors_documentation_en-US" xlink:label="lab_kg_NumberOfDirectors" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Directors</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfDirectors" xlink:href="kg-20260630.xsd#kg_NumberOfDirectors"/>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteAbstract_019e18df-79c7-74d0-ba90-dca7188dc18f_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Note [Abstract]</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Note [Abstract]</link:label>
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    <link:label id="lab_kg_LukeLedbetterMember_019e18df-79c7-7cf3-ae2f-906dccd430d3_terseLabel_en-US" xlink:label="lab_kg_LukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Luke Ledbetter</link:label>
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    <link:label id="lab_kg_LukeLedbetterMember_documentation_en-US" xlink:label="lab_kg_LukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Luke Ledbetter</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LukeLedbetterMember" xlink:to="lab_kg_LukeLedbetterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_019e18df-79c7-73e7-930e-d09e65fe835e_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain"/>
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    <link:label id="lab_kg_SeniorNotes2013Member_019e18df-7903-7c5a-adf0-a5bc66185cf3_verboseLabel_en-US" xlink:label="lab_kg_SeniorNotes2013Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes - MHNC &#8211; 7.75%</link:label>
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    <link:label id="lab_kg_SeniorNotes2013Member_documentation_en-US" xlink:label="lab_kg_SeniorNotes2013Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes 2013 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2013Member" xlink:href="kg-20260630.xsd#kg_SeniorNotes2013Member"/>
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    <link:label id="lab_us-gaap_CededCreditRiskAxis_019e18df-79c7-7a63-b41f-17d544182fc3_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Axis]</link:label>
    <link:label id="lab_us-gaap_CededCreditRiskAxis_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededCreditRiskAxis" xlink:to="lab_us-gaap_CededCreditRiskAxis" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal" xlink:href="kg-20260630.xsd#kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal" xlink:to="lab_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_019e18df-79c7-7a1c-91d5-1b72eb2d686a_terseLabel_en-US" xlink:label="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policy inception, grace period</link:label>
    <link:label id="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_label_en-US" xlink:label="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Contracts, Program Fee Receivables, Premium Receivable, Collection Period</link:label>
    <link:label id="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_documentation_en-US" xlink:label="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Contracts, Program Fee Receivables, Premium Receivable, Collection Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:href="kg-20260630.xsd#kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:to="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_019e18df-79c7-720e-a6de-b6f2436a7470_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_019e18df-79c7-7c46-add3-0f29907f9c57_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_019e18df-79c7-7af9-be71-29ace9887b86_netLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_019e18df-79c7-73a4-aab3-7c4416c8a680_totalLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_label_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PremiumsWrittenNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsWrittenNet" xlink:to="lab_us-gaap_PremiumsWrittenNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock_019e18df-79c6-7507-b9cf-2133f7e6801d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value of Restricted Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Owned and Pledged as Collateral [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:to="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceAgreementOpen_019e18df-7903-7158-8e6c-eecbe71b64fd_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceAgreementOpen" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reinsurance agreements, open</link:label>
    <link:label id="lab_kg_ReinsuranceAgreementOpen_label_en-US" xlink:label="lab_kg_ReinsuranceAgreementOpen" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Agreement, Open</link:label>
    <link:label id="lab_kg_ReinsuranceAgreementOpen_documentation_en-US" xlink:label="lab_kg_ReinsuranceAgreementOpen" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Agreement, Open</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceAgreementOpen" xlink:href="kg-20260630.xsd#kg_ReinsuranceAgreementOpen"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceAgreementOpen" xlink:to="lab_kg_ReinsuranceAgreementOpen" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_019e18df-7a58-7ae0-88ae-89a453251774_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments and Carrying Value and Beneficial Ownership Percentage of Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RealizedAndUnrealizedLossOnInvestments_019e18df-7903-7f42-ab62-d4f0ac55914c_negatedTotalLabel_en-US" xlink:label="lab_kg_RealizedAndUnrealizedLossOnInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized gains (losses) on investment, gross losses</link:label>
    <link:label id="lab_kg_RealizedAndUnrealizedLossOnInvestments_label_en-US" xlink:label="lab_kg_RealizedAndUnrealizedLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized And Unrealized Loss On Investments</link:label>
    <link:label id="lab_kg_RealizedAndUnrealizedLossOnInvestments_documentation_en-US" xlink:label="lab_kg_RealizedAndUnrealizedLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Realized And Unrealized Loss On Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealizedAndUnrealizedLossOnInvestments" xlink:href="kg-20260630.xsd#kg_RealizedAndUnrealizedLossOnInvestments"/>
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    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
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    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_019e18df-7903-7ce2-9aad-6fcd06edd875_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. agency bonds&#160;&#8211;&#160;mortgage-backed</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage-Backed Security, Issued by US Government-Sponsored Enterprise [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
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    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness_019e18df-7a57-7f20-9d6e-b09cba2bdb17_negatedTerseLabel_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net Maiden Legacy run-off business acquired</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness_label_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Assumed Business</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness_documentation_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Assumed Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness" xlink:href="kg-20260630.xsd#kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_019e18df-79c7-77ad-9159-d24499828baf_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Sales</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales"/>
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    <link:label id="lab_us-gaap_AssumedPremiumsWritten_019e18df-79c6-7838-bb76-83e7dd198e2a_terseLabel_en-US" xlink:label="lab_us-gaap_AssumedPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed</link:label>
    <link:label id="lab_us-gaap_AssumedPremiumsWritten_label_en-US" xlink:label="lab_us-gaap_AssumedPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assumed Premiums Written</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssumedPremiumsWritten" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssumedPremiumsWritten"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssumedPremiumsWritten" xlink:to="lab_us-gaap_AssumedPremiumsWritten" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_019e18df-7903-77a6-b9e2-58feeae7f889_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain on bargain purchase</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_019e18df-7903-7728-83a2-4daee18d6f6c_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gain on bargain purchase</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_019e18df-7903-7d13-bdd1-d13e8a3121ae_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on bargain purchase</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_019e18df-7903-7c16-a7ab-aa39aae445d6_negatedLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Bargain purchase gain</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Bargain Purchase, Gain Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:to="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_019e18df-79c7-7763-aa7c-3b9d25e91fca_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock_019e18df-7903-7b06-a8e1-08c846ac3ad2_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross equity portion of consideration transferred at Closing</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock_label_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest, Excluding Treasury Stock</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest, Excluding Treasury Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock" xlink:href="kg-20260630.xsd#kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock" xlink:to="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestExcludingTreasuryStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_019e18df-79c7-7fee-b1cc-b855aee69631_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_019e18df-7a57-749c-bc7c-52e8f57d5467_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationFairValueAssessmentAxis_019fd799-3b8a-75c7-8744-ce523f974f0e_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationFairValueAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Fair Value Assessment [Axis]</link:label>
    <link:label id="lab_kg_BusinessCombinationFairValueAssessmentAxis_label_en-US" xlink:label="lab_kg_BusinessCombinationFairValueAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Fair Value Assessment [Axis]</link:label>
    <link:label id="lab_kg_BusinessCombinationFairValueAssessmentAxis_documentation_en-US" xlink:label="lab_kg_BusinessCombinationFairValueAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Fair Value Assessment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationFairValueAssessmentAxis" xlink:href="kg-20260630.xsd#kg_BusinessCombinationFairValueAssessmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationFairValueAssessmentAxis" xlink:to="lab_kg_BusinessCombinationFairValueAssessmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainContingenciesLineItems_019e18df-7903-730b-af9a-52132757f392_terseLabel_en-US" xlink:label="lab_us-gaap_GainContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_GainContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_GainContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainContingenciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainContingenciesLineItems" xlink:to="lab_us-gaap_GainContingenciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019e18df-7903-7ec6-9d3c-27c1bbb61203_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
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    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_019e18df-79c7-7106-b909-9dbd920abf94_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
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    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_019e18df-79c7-797a-ae65-3784469cd003_terseLabel_en-US" xlink:label="lab_kg_LegacyReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legacy Reinsurance</link:label>
    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_019e18df-79c7-764c-b226-5a84363ad54b_verboseLabel_en-US" xlink:label="lab_kg_LegacyReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Legacy Reinsurance Segment</link:label>
    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_LegacyReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legacy Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_LegacyReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Legacy Reinsurance Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LegacyReinsuranceSegmentMember" xlink:href="kg-20260630.xsd#kg_LegacyReinsuranceSegmentMember"/>
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    <link:label id="lab_us-gaap_CommonStockSharesIssued_019e18df-79c7-7d72-971e-5ac294aa75f9_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019e18df-7a57-7399-b30d-ab1418c2be8d_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance - beginning of period</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
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    <link:label id="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims_019e18df-7a57-765c-840e-e9fc49cb6be4_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional claims estimated</link:label>
    <link:label id="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims_label_en-US" xlink:label="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Incurred but Not Reported Claims</link:label>
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    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract_019e18df-79c7-7642-9cd5-812eb841ff8c_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Fair Value [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract"/>
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    <link:label id="lab_us-gaap_LoansPayable_019e18df-7903-7120-a625-ed5617205426_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance principal amount</link:label>
    <link:label id="lab_us-gaap_LoansPayable_label_en-US" xlink:label="lab_us-gaap_LoansPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansPayable"/>
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    <link:label id="lab_kg_TreasuryStockSharesIssuedToSubsidiary_019e18df-79c6-7ae7-b12e-9bcdbd9680e7_negatedTerseLabel_en-US" xlink:label="lab_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares issued to Maiden Reinsurance</link:label>
    <link:label id="lab_kg_TreasuryStockSharesIssuedToSubsidiary_label_en-US" xlink:label="lab_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares Issued to Subsidiary</link:label>
    <link:label id="lab_kg_TreasuryStockSharesIssuedToSubsidiary_documentation_en-US" xlink:label="lab_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares Issued to Subsidiary</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:href="kg-20260630.xsd#kg_TreasuryStockSharesIssuedToSubsidiary"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:to="lab_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_019e18df-7903-745f-bc96-f80af17f10e2_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums_019e18df-79c7-7e1a-8b58-46dc0b5e639b_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commission rate, percent of ceded written premiums</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Percent of Ceded Written Premiums</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Percent of Ceded Written Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:to="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019e18df-7a58-7647-a4f6-c77a72ce5968_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract_019e18df-79c6-7488-b235-74b765cb46a0_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Identifiable Intangible Asset, Excluding Goodwill [Abstract]</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_019e18df-79c7-7b00-b4bb-03e3f14f8eb2_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_019e18df-79c7-72ff-86d0-4eb846cf528f_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationFairValueAssessmentDomain_019fd799-3b8a-7f23-9272-5a3a96f2c2e9_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationFairValueAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Fair Value Assessment [Domain]</link:label>
    <link:label id="lab_kg_BusinessCombinationFairValueAssessmentDomain_label_en-US" xlink:label="lab_kg_BusinessCombinationFairValueAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Fair Value Assessment [Domain]</link:label>
    <link:label id="lab_kg_BusinessCombinationFairValueAssessmentDomain_documentation_en-US" xlink:label="lab_kg_BusinessCombinationFairValueAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Fair Value Assessment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationFairValueAssessmentDomain" xlink:href="kg-20260630.xsd#kg_BusinessCombinationFairValueAssessmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationFairValueAssessmentDomain" xlink:to="lab_kg_BusinessCombinationFairValueAssessmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019e18df-79c7-751b-bb22-00df70e4fff8_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AELMember_019e18df-79c7-78e9-af3c-a47028ba3a7d_terseLabel_en-US" xlink:label="lab_kg_AELMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AEL</link:label>
    <link:label id="lab_kg_AELMember_label_en-US" xlink:label="lab_kg_AELMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AEL [Member]</link:label>
    <link:label id="lab_kg_AELMember_documentation_en-US" xlink:label="lab_kg_AELMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AEL [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AELMember" xlink:href="kg-20260630.xsd#kg_AELMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AELMember" xlink:to="lab_kg_AELMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PremiumsEarnedNetAsPercentOfTotal_019e18df-7a57-7731-b367-8fa79fa2b7ba_terseLabel_en-US" xlink:label="lab_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of total net premiums earned</link:label>
    <link:label id="lab_kg_PremiumsEarnedNetAsPercentOfTotal_label_en-US" xlink:label="lab_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Earned, Net as a Percent of Total</link:label>
    <link:label id="lab_kg_PremiumsEarnedNetAsPercentOfTotal_documentation_en-US" xlink:label="lab_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premiums Earned, Net as a Percent of Total</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:href="kg-20260630.xsd#kg_PremiumsEarnedNetAsPercentOfTotal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:to="lab_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_019e18df-79c6-77b0-b34f-8692c741427a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss from discontinued operations, net of income tax</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:to="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_019e18df-7903-75b6-98df-5d3b759eceba_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense_019e18df-79c7-7884-bb13-4fcfd096afed_verboseLabel_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net incurred losses related to Current year</link:label>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Year Claims and Claims Adjustment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:to="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesPercentofTotalFairValue_019e18df-7903-7401-93c3-f9cc5845b336_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesPercentofTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of Total fair value</link:label>
    <link:label id="lab_kg_FixedMaturitiesPercentofTotalFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesPercentofTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Percent of Total Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesPercentofTotalFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesPercentofTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Percent of Total Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesPercentofTotalFairValue" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesPercentofTotalFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesPercentofTotalFairValue" xlink:to="lab_kg_FixedMaturitiesPercentofTotalFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquityMethodInvestmentsPercentOfTotal_019e18df-7a58-782f-8c64-e70f28d81aa7_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of Total</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsPercentOfTotal_label_en-US" xlink:label="lab_kg_EquityMethodInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Percent Of Total</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsPercentOfTotal_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Percent Of Total</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsPercentOfTotal" xlink:href="kg-20260630.xsd#kg_EquityMethodInvestmentsPercentOfTotal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquityMethodInvestmentsPercentOfTotal" xlink:to="lab_kg_EquityMethodInvestmentsPercentOfTotal" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_019e18df-79c7-7806-981a-1969f4e79a9f_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of losses with respect to current lines of business, excluding those above covered business threshold to related party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Losses With Respect to Current Lines of Business, Excluding Those Above Covered Business Threshold To Related Party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Losses With Respect to Current Lines of Business, Excluding Those Above Covered Business Threshold To Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:to="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_019e18df-7a57-7fa8-acbe-9d9da88953ce_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption price, percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedInvestmentLiability_019e18df-7a57-7d90-91ea-2296f5ab7f73_negatedTerseLabel_en-US" xlink:label="lab_kg_RestrictedInvestmentLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Restricted investments &#8211; receivable for investments sold under related party agreements</link:label>
    <link:label id="lab_kg_RestrictedInvestmentLiability_label_en-US" xlink:label="lab_kg_RestrictedInvestmentLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Investment, Liability</link:label>
    <link:label id="lab_kg_RestrictedInvestmentLiability_documentation_en-US" xlink:label="lab_kg_RestrictedInvestmentLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Investment, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedInvestmentLiability" xlink:href="kg-20260630.xsd#kg_RestrictedInvestmentLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RestrictedInvestmentLiability" xlink:to="lab_kg_RestrictedInvestmentLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses_019e18df-79c7-72a4-abd2-8f2d33e1b8f3_negatedTerseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and loss adjustment expenses</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Reserve For Loss And Loss Adjustment Expenses</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Reserve For Loss And Loss Adjustment Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_019e18df-7902-7cd3-b8b0-e600917a720b_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019e18df-79c6-72af-8a19-5a02ec7c7b0c_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019e18df-7a57-7ee5-8cca-e5aea8306b8b_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FundsWithheldArrangementMember_019e18df-7a57-7f02-a98e-4ec4645cb239_terseLabel_en-US" xlink:label="lab_kg_FundsWithheldArrangementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income on funds withheld</link:label>
    <link:label id="lab_kg_FundsWithheldArrangementMember_label_en-US" xlink:label="lab_kg_FundsWithheldArrangementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Funds Withheld Arrangement [Member]</link:label>
    <link:label id="lab_kg_FundsWithheldArrangementMember_documentation_en-US" xlink:label="lab_kg_FundsWithheldArrangementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Funds Withheld Arrangement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FundsWithheldArrangementMember" xlink:href="kg-20260630.xsd#kg_FundsWithheldArrangementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FundsWithheldArrangementMember" xlink:to="lab_kg_FundsWithheldArrangementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivateCreditLendingMember_019e18df-79c7-708f-9b75-a7d4809f4cde_verboseLabel_en-US" xlink:label="lab_kg_PrivateCreditLendingMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Private credit investments</link:label>
    <link:label id="lab_kg_PrivateCreditLendingMember_label_en-US" xlink:label="lab_kg_PrivateCreditLendingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Credit Lending [Member]</link:label>
    <link:label id="lab_kg_PrivateCreditLendingMember_documentation_en-US" xlink:label="lab_kg_PrivateCreditLendingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Credit Lending</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivateCreditLendingMember" xlink:href="kg-20260630.xsd#kg_PrivateCreditLendingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivateCreditLendingMember" xlink:to="lab_kg_PrivateCreditLendingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_019e18df-7a57-74d1-9529-d435a25748a7_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable, allowance for credit loss</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_019e18df-7a57-718d-9870-5f9a39c1daba_periodStartLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses on reinsurance recoverable, beginning of period</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_019e18df-7a57-70b1-a8bf-078240642e82_periodEndLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses on reinsurance recoverable, end of period</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverablesAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesAllowance" xlink:to="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PremiumRepaymentLoanAgreementMember_019e18df-7903-7b69-9df3-53446b52599d_terseLabel_en-US" xlink:label="lab_kg_PremiumRepaymentLoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premium Repayment Loan Agreement</link:label>
    <link:label id="lab_kg_PremiumRepaymentLoanAgreementMember_label_en-US" xlink:label="lab_kg_PremiumRepaymentLoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Repayment Loan Agreement [Member]</link:label>
    <link:label id="lab_kg_PremiumRepaymentLoanAgreementMember_documentation_en-US" xlink:label="lab_kg_PremiumRepaymentLoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premium Repayment Loan Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumRepaymentLoanAgreementMember" xlink:href="kg-20260630.xsd#kg_PremiumRepaymentLoanAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PremiumRepaymentLoanAgreementMember" xlink:to="lab_kg_PremiumRepaymentLoanAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_019e18df-7903-750d-b900-274d968333a9_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MarketableSecuritiesRealizedGain_019e18df-79c6-7476-801a-25b3e63f1a8f_terseLabel_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedGain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments, gross gains</link:label>
    <link:label id="lab_kg_MarketableSecuritiesRealizedGain_label_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedGain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Realized Gain</link:label>
    <link:label id="lab_kg_MarketableSecuritiesRealizedGain_documentation_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedGain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketable Securities, Realized Gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MarketableSecuritiesRealizedGain" xlink:href="kg-20260630.xsd#kg_MarketableSecuritiesRealizedGain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MarketableSecuritiesRealizedGain" xlink:to="lab_kg_MarketableSecuritiesRealizedGain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019e18df-7a58-77df-84b1-57ba0516fe83_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest in income of equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019e18df-7a58-797d-98ed-8eb0d4096424_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest in income of equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AlternativeInvestment_019e18df-7a57-75d7-b6d4-37c6f363c207_terseLabel_en-US" xlink:label="lab_us-gaap_AlternativeInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_us-gaap_AlternativeInvestment_label_en-US" xlink:label="lab_us-gaap_AlternativeInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Alternative Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AlternativeInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AlternativeInvestment" xlink:to="lab_us-gaap_AlternativeInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_019e18df-7903-74a5-bc0f-07ecfa4c848d_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum limit of liability attaching</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Maximum Limit of Liability Attaching</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Maximum Limit of Liability Attaching</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:to="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_019e18df-7903-7695-805f-731ac31fe5cc_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total before securities with single maturities, fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract_019e18df-7a58-72c9-bc81-2e6903126ffd_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in liabilities &#8211; increase (decrease):</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_019e18df-79c7-7eaf-b144-d411ef781440_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentOwnershipAtMergerClosingMember_019e18df-7902-7c48-a00f-25bc63dfe358_terseLabel_en-US" xlink:label="lab_kg_InvestmentOwnershipAtMergerClosingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Ownership, Issued at closing of Combination</link:label>
    <link:label id="lab_kg_InvestmentOwnershipAtMergerClosingMember_label_en-US" xlink:label="lab_kg_InvestmentOwnershipAtMergerClosingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Ownership, At Merger Closing [Member]</link:label>
    <link:label id="lab_kg_InvestmentOwnershipAtMergerClosingMember_documentation_en-US" xlink:label="lab_kg_InvestmentOwnershipAtMergerClosingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Ownership, At Merger Closing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnershipAtMergerClosingMember" xlink:href="kg-20260630.xsd#kg_InvestmentOwnershipAtMergerClosingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentOwnershipAtMergerClosingMember" xlink:to="lab_kg_InvestmentOwnershipAtMergerClosingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_019e18df-7a57-7642-9afa-d467cf3578a5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Measured at Fair Value on a Recurring Basis</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_019e18df-7903-7b8c-9e32-a9ba225b5953_terseLabel_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_label_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Payments Due After Year Four</link:label>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_documentation_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Payments Due After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:href="kg-20260630.xsd#kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:to="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019e18df-7903-7554-8e4a-e000f38d556d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_019e18df-79c7-70d1-89b8-5b6c583a16a1_verboseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceAgreementCompletingRunOff_019e18df-79c7-7839-b52f-36e11022b0f3_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceAgreementCompletingRunOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reinsurance agreements, completing run-off</link:label>
    <link:label id="lab_kg_ReinsuranceAgreementCompletingRunOff_label_en-US" xlink:label="lab_kg_ReinsuranceAgreementCompletingRunOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Agreement, Completing Run-Off</link:label>
    <link:label id="lab_kg_ReinsuranceAgreementCompletingRunOff_documentation_en-US" xlink:label="lab_kg_ReinsuranceAgreementCompletingRunOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Agreement, Completing Run-Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceAgreementCompletingRunOff" xlink:href="kg-20260630.xsd#kg_ReinsuranceAgreementCompletingRunOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceAgreementCompletingRunOff" xlink:to="lab_kg_ReinsuranceAgreementCompletingRunOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019e18df-79c6-76f3-9564-d57c54d0921f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019e18df-79c6-762d-a3bd-efceb4134d27_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_019e18df-79c7-77dd-b4ff-d4b8d575c10f_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. agency bonds&#160;&#8211;&#160;mortgage-backed</link:label>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Agencies Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_USGovernmentAgenciesDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019e18df-79c7-728e-99de-9552288b35b3_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_019e18df-7903-713c-8429-64cf27ab6a2c_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock repurchased (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_label_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares, Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockSharesAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockSharesAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockSharesAcquired" xlink:to="lab_us-gaap_TreasuryStockSharesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_019e18df-79c7-734e-b19c-5c46d4595b47_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, operating lease, term of contract</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseTermOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:to="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_019e18df-7a57-7b2a-89d9-21e2bd977039_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minority interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVenture3Member_019e18df-7903-72d6-931d-05b08ad05690_terseLabel_en-US" xlink:label="lab_kg_SilverstoneVenture3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Silverstone Venture 3</link:label>
    <link:label id="lab_kg_SilverstoneVenture3Member_label_en-US" xlink:label="lab_kg_SilverstoneVenture3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Silverstone Venture 3 [Member]</link:label>
    <link:label id="lab_kg_SilverstoneVenture3Member_documentation_en-US" xlink:label="lab_kg_SilverstoneVenture3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Silverstone Venture 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVenture3Member" xlink:href="kg-20260630.xsd#kg_SilverstoneVenture3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SilverstoneVenture3Member" xlink:to="lab_kg_SilverstoneVenture3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense_019e18df-7902-7671-9414-ca4cf3c3a185_totalLabel_en-US" xlink:label="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains, net of deferred income tax</link:label>
    <link:label id="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense_label_en-US" xlink:label="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Gross Unrealized Gain (Loss), Net of Deferred Income Tax Expense</link:label>
    <link:label id="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense_documentation_en-US" xlink:label="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Gross Unrealized Gain (Loss), Net of Deferred Income Tax Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:href="kg-20260630.xsd#kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:to="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_019e18df-79c6-7198-8220-4d13385be3cc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Based on NAV Practical Expedient</link:label>
    <link:label id="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measured at Net Asset Value Per Share [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:to="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ScheduleofFixedMaturitiesTableLineItems_019e18df-7902-7158-9ea1-54efc822246f_terseLabel_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fixed Maturities Table [Line Items]</link:label>
    <link:label id="lab_kg_ScheduleofFixedMaturitiesTableLineItems_label_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fixed Maturities Table [Line Items]</link:label>
    <link:label id="lab_kg_ScheduleofFixedMaturitiesTableLineItems_documentation_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for Schedule of Fixed Maturities Table [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:href="kg-20260630.xsd#kg_ScheduleofFixedMaturitiesTableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:to="lab_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_019e18df-7902-74e7-9f2d-3be74cc1b4d6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019e18df-7903-79d0-a03b-a7618e326ebe_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_019e18df-7a57-7807-8759-4df4c088c990_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest and amortization expenses</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelIntermediateLedbetterHoldingsMember_019e18df-79c7-72b7-91c6-e13d39af3870_terseLabel_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings</link:label>
    <link:label id="lab_kg_KestrelIntermediateLedbetterHoldingsMember_label_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings [Member]</link:label>
    <link:label id="lab_kg_KestrelIntermediateLedbetterHoldingsMember_documentation_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:href="kg-20260630.xsd#kg_KestrelIntermediateLedbetterHoldingsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:to="lab_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_019e18df-7903-764b-956c-85310c8560c1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased</link:label>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_label_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Value, Acquired, Cost Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockValueAcquiredCostMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:to="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e18df-79c7-76af-9552-02ed2d6f8de5_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, restricted cash and cash equivalents, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e18df-79c7-7340-b0d5-2faef99aaf43_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, restricted cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e18df-79c7-7efa-9e15-6a03ecde63fd_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total cash, restricted cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockOwnershipDomain_019e18df-7a57-70f9-921e-161faa05ba3e_terseLabel_en-US" xlink:label="lab_kg_CommonStockOwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock Ownership [Domain]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipDomain_label_en-US" xlink:label="lab_kg_CommonStockOwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Ownership [Domain]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipDomain_documentation_en-US" xlink:label="lab_kg_CommonStockOwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockOwnershipDomain" xlink:href="kg-20260630.xsd#kg_CommonStockOwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommonStockOwnershipDomain" xlink:to="lab_kg_CommonStockOwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember_019e18df-79c7-7f50-9f00-66ac281b098e_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Value Change - Market/Industry Factors</link:label>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember_label_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Change in Guideline Public Company TIC [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Change in Guideline Public Company TIC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:href="kg-20260630.xsd#kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:to="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_019e18df-7a58-7072-bf60-5738871f3cda_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Upfront cash</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_019e18df-7a57-734e-b34c-e8952ebc7d0a_verboseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Ownership percentage</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_019e18df-7a57-7b67-aa3b-ff3fd81e6315_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Beneficial Ownership</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_019e18df-7a58-7e0e-9150-6e0950875223_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_HistoricReinsuranceMember_019e18df-7a57-7776-a6fb-36db37abb7c0_terseLabel_en-US" xlink:label="lab_kg_HistoricReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Historic Reinsurance</link:label>
    <link:label id="lab_kg_HistoricReinsuranceMember_label_en-US" xlink:label="lab_kg_HistoricReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Historic Reinsurance [Member]</link:label>
    <link:label id="lab_kg_HistoricReinsuranceMember_documentation_en-US" xlink:label="lab_kg_HistoricReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Historic Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_HistoricReinsuranceMember" xlink:href="kg-20260630.xsd#kg_HistoricReinsuranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_HistoricReinsuranceMember" xlink:to="lab_kg_HistoricReinsuranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelGroupCommonStockMember_019e18df-79c7-701f-ada8-36d805330324_terseLabel_en-US" xlink:label="lab_kg_KestrelGroupCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group, Common Stock</link:label>
    <link:label id="lab_kg_KestrelGroupCommonStockMember_label_en-US" xlink:label="lab_kg_KestrelGroupCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Group, Common Stock [Member]</link:label>
    <link:label id="lab_kg_KestrelGroupCommonStockMember_documentation_en-US" xlink:label="lab_kg_KestrelGroupCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Group, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupCommonStockMember" xlink:href="kg-20260630.xsd#kg_KestrelGroupCommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelGroupCommonStockMember" xlink:to="lab_kg_KestrelGroupCommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_019e18df-79c7-7b37-b6ad-30aca97cae0a_terseLabel_en-US" xlink:label="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of outstanding debt holders in lawsuit (at least)</link:label>
    <link:label id="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_label_en-US" xlink:label="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Percentage of Outstanding Debt Holders Involved in Lawsuit</link:label>
    <link:label id="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_documentation_en-US" xlink:label="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Contingency, Percentage of Outstanding Debt Holders Involved in Lawsuit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:href="kg-20260630.xsd#kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:to="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_019e18df-79c7-79a8-9854-dc5e23e0de46_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EquityMethodInvesteeNameDomain" xlink:to="lab_srt_EquityMethodInvesteeNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019e18df-7903-73c2-b889-483fc779b99e_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_019e18df-7902-774e-984e-5e424c9b013a_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_019e18df-7902-74a5-81ca-08ed32c37356_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchase of common shares</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentMilestoneTypeAxis_019e18df-7903-7239-896e-596530ef2954_terseLabel_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Axis]</link:label>
    <link:label id="lab_kg_InvestmentMilestoneTypeAxis_label_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Axis]</link:label>
    <link:label id="lab_kg_InvestmentMilestoneTypeAxis_documentation_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentMilestoneTypeAxis" xlink:href="kg-20260630.xsd#kg_InvestmentMilestoneTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentMilestoneTypeAxis" xlink:to="lab_kg_InvestmentMilestoneTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019e18df-79c7-7d4a-b5c6-95354af34c22_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy_019e18df-79c7-7dfb-8c5d-1552305065ba_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance, excess retention, amount reinsured, per policy</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Excess Retention, Amount Reinsured, Per Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:to="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementNo.1Member_019e18df-7903-796a-a9f3-cf7bc7d4f219_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 1</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementNo.1Member_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 1 [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementNo.1Member_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementNo.1Member" xlink:href="kg-20260630.xsd#kg_PostTerminationEndorsementNo.1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementNo.1Member" xlink:to="lab_kg_PostTerminationEndorsementNo.1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_019e18df-7903-7cfa-a93e-614807db5989_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019e18df-7a57-7450-b07c-eded2a442f52_verboseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">(Accumulated deficit) retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementMember_019e18df-79c6-7dee-ba79-b58d9fc458ea_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMember_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMember_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMember" xlink:href="kg-20260630.xsd#kg_PostTerminationEndorsementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementMember" xlink:to="lab_kg_PostTerminationEndorsementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019e18df-79c7-7580-be16-9c420c768650_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_019e18df-79c7-73ac-a8b5-cfee6f6f230c_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total equity securities subject to contractual sale restrictions</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:to="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019e18df-7903-79c1-8607-14775f38461d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_019e18df-7903-782a-a62a-5863ab2cddd2_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Privately held common stocks</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_019e18df-7903-7737-95d2-b9deb02c6771_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities: available-for-sale, at fair value (Amortized cost: 2026: $144,533; 2025: $168,991)</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_019e18df-7903-7523-bb33-48c7fc656545_netLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_019e18df-7903-7dd9-92b8-5bf8eda6cced_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_019e18df-7903-79b9-bd10-a1f7e0a4de08_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted_019e18df-79c6-76f8-ba2c-0cbd6d4ae128_terseLabel_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative arrangement, reserves expected to be commuted</link:label>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted_label_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Reserves Expected to be Commuted</link:label>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted_documentation_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Reserves Expected to be Commuted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:href="kg-20260630.xsd#kg_CollaborativeArrangementReservesExpectedToBeCommuted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:to="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1_019fcfa3-4c54-7deb-b08e-23fcb0e2ed80_negatedLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Change in Contingent Consideration, Asset, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_019e18df-79c7-7baa-95f6-891c2224190c_terseLabel_en-US" xlink:label="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">A+, A, A-</link:label>
    <link:label id="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_label_en-US" xlink:label="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's SingleA Plus, SingleA, and SingleA Minus [Member]</link:label>
    <link:label id="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_documentation_en-US" xlink:label="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, A-Plus, A, A- Rating [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:href="kg-20260630.xsd#kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:to="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019e18df-7a57-784e-8df4-e7761571ba96_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements_019e18df-7a57-798e-b706-3f397a2e5d80_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Funds withheld receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Funds Held under Reinsurance Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements" xlink:to="lab_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_019e18df-7a58-7e89-baa4-84d9d34593b3_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, net</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019e18df-7a57-7672-9e4a-53c4d74b986d_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NumberOfIndependentDirectors_019e18df-79c6-7dfd-b117-905988c463c7_terseLabel_en-US" xlink:label="lab_kg_NumberOfIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of independent directors</link:label>
    <link:label id="lab_kg_NumberOfIndependentDirectors_label_en-US" xlink:label="lab_kg_NumberOfIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Independent Directors</link:label>
    <link:label id="lab_kg_NumberOfIndependentDirectors_documentation_en-US" xlink:label="lab_kg_NumberOfIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Independent Directors</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfIndependentDirectors" xlink:href="kg-20260630.xsd#kg_NumberOfIndependentDirectors"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NumberOfIndependentDirectors" xlink:to="lab_kg_NumberOfIndependentDirectors" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill_019e18df-7903-7e62-9965-74127a598686_verboseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill_019e18df-7903-77b6-a12f-196d44b81bcd_netLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Intangible assets, net</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Including Goodwill, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsNetIncludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MiscellaneousInvestmentsMember_019e18eb-368e-76ce-be44-827ede3fc8ea_terseLabel_en-US" xlink:label="lab_us-gaap_MiscellaneousInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other equity method investments at fair value option elected</link:label>
    <link:label id="lab_us-gaap_MiscellaneousInvestmentsMember_019e18ed-a928-7d5a-9971-6037c67ed34c_verboseLabel_en-US" xlink:label="lab_us-gaap_MiscellaneousInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Investments</link:label>
    <link:label id="lab_us-gaap_MiscellaneousInvestmentsMember_019e18f0-a7c4-7f04-a4c0-7b07a77fca50_netLabel_en-US" xlink:label="lab_us-gaap_MiscellaneousInvestmentsMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total unfunded commitments on other investments</link:label>
    <link:label id="lab_us-gaap_MiscellaneousInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_MiscellaneousInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Miscellaneous Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MiscellaneousInvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MiscellaneousInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MiscellaneousInvestmentsMember" xlink:to="lab_us-gaap_MiscellaneousInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_019e18df-7a58-7ed2-9165-7efebf7a9897_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Options</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_019e18df-79c7-7e7d-b62d-a9e1dca8a48d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_019e18df-79c7-7774-9b0f-7de6c42da5f6_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards expire</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsTable_019e18df-79c6-7fdc-8b0e-882317fb19f9_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Table]</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsTable_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLossCarryforwardsTable"/>
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    <link:label id="lab_kg_GeorgeKarfunkelMember_019e18df-7a57-7f68-83f2-c19dc7f6188c_terseLabel_en-US" xlink:label="lab_kg_GeorgeKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">George Karfunkel</link:label>
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    <link:label id="lab_kg_GeorgeKarfunkelMember_documentation_en-US" xlink:label="lab_kg_GeorgeKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">George Karfunkel [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GeorgeKarfunkelMember" xlink:to="lab_kg_GeorgeKarfunkelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019e18df-7a57-71e4-a7b0-e1810a635c70_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019e18df-7a57-705c-aef7-176a1d713b48_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019e18df-7a57-7089-812d-e161dcc30b48_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_019e18df-7903-7bca-9d03-a12913de3eb8_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses: (Allowance for expected credit losses: 2026: $1,613; 2025: $1,740)</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_019e18df-7903-714c-96fa-a9779c21210e_verboseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable for Unpaid Claims and Claims Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments"/>
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    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock_019e18df-79c7-799a-bb7f-1fc82d058095_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Unrealized Losses Included in Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable_019e18df-79c7-7819-b4ab-a3954a95c424_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Reinsurance Recoverable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInReinsuranceRecoverable"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_019e18df-7a57-7018-adb3-f5a2b36ebbb2_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_019e18df-7903-731d-b4c4-12e60c987404_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_us-gaap_CededPremiumsWritten_019e18df-7a57-75bd-bd57-f03ab0c3590b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CededPremiumsWritten" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Ceded</link:label>
    <link:label id="lab_us-gaap_CededPremiumsWritten_label_en-US" xlink:label="lab_us-gaap_CededPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ceded Premiums Written</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededPremiumsWritten" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CededPremiumsWritten"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededPremiumsWritten" xlink:to="lab_us-gaap_CededPremiumsWritten" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock_019e18df-7903-7dda-9627-139118def937_terseLabel_en-US" xlink:label="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cost and Fair Values of the Equity Securities and Privately Held Securities Held Subject to Contractual Sale Restrictions</link:label>
    <link:label id="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock_label_en-US" xlink:label="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:to="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue_019e18df-79c7-795c-913d-b417e64db1cf_terseLabel_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets, fair value disclosure, number of securities priced for fair value</link:label>
    <link:label id="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue_label_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure, Number Of Securities Priced For Fair Value</link:label>
    <link:label id="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue_documentation_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure, Number Of Securities Priced For Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:href="kg-20260630.xsd#kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:to="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:href="kg-20260630.xsd#kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:to="lab_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_019e18df-7903-7c7e-9ec9-9e8aad798019_negatedTerseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Liabilities held for sale</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Liabilities Held For Sale</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Liabilities Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentOwnership5PercentMember_019e18df-79c7-781b-ab4a-83338d7d0661_terseLabel_en-US" xlink:label="lab_kg_InvestmentOwnership5PercentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Ownership, 5%</link:label>
    <link:label id="lab_kg_InvestmentOwnership5PercentMember_label_en-US" xlink:label="lab_kg_InvestmentOwnership5PercentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Ownership, 5 Percent [Member]</link:label>
    <link:label id="lab_kg_InvestmentOwnership5PercentMember_documentation_en-US" xlink:label="lab_kg_InvestmentOwnership5PercentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Ownership, 5 Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnership5PercentMember" xlink:href="kg-20260630.xsd#kg_InvestmentOwnership5PercentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentOwnership5PercentMember" xlink:to="lab_kg_InvestmentOwnership5PercentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentOwnership25PercentMember_019e18df-7a57-7d13-b3f5-93190d574688_terseLabel_en-US" xlink:label="lab_kg_InvestmentOwnership25PercentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Ownership, 25%</link:label>
    <link:label id="lab_kg_InvestmentOwnership25PercentMember_label_en-US" xlink:label="lab_kg_InvestmentOwnership25PercentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Ownership, 25 Percent [Member]</link:label>
    <link:label id="lab_kg_InvestmentOwnership25PercentMember_documentation_en-US" xlink:label="lab_kg_InvestmentOwnership25PercentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Ownership, 25 Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnership25PercentMember" xlink:href="kg-20260630.xsd#kg_InvestmentOwnership25PercentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentOwnership25PercentMember" xlink:to="lab_kg_InvestmentOwnership25PercentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RealEstateInvestmentsAtFairValueMember_019e18df-79c7-74b2-be28-ea3f6e160f84_terseLabel_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate investments at fair value option elected</link:label>
    <link:label id="lab_kg_RealEstateInvestmentsAtFairValueMember_label_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investments At Fair Value [Member]</link:label>
    <link:label id="lab_kg_RealEstateInvestmentsAtFairValueMember_documentation_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Investments At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealEstateInvestmentsAtFairValueMember" xlink:href="kg-20260630.xsd#kg_RealEstateInvestmentsAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RealEstateInvestmentsAtFairValueMember" xlink:to="lab_kg_RealEstateInvestmentsAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic_019e18df-7903-71b7-8ae6-ffa26faa7aa6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amount allocated to participating common shareholders, basic</link:label>
    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic_label_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Participating Securities, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:to="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019e18df-7902-7b88-bb26-56d6c94d5908_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total investments</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019e18df-7902-7686-936a-07f6bf344ed9_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments, fair value</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MaidenHoldingsLtd.Member_019e18df-7903-7b85-901c-6597d944736f_terseLabel_en-US" xlink:label="lab_kg_MaidenHoldingsLtd.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maiden Holdings, Ltd.</link:label>
    <link:label id="lab_kg_MaidenHoldingsLtd.Member_label_en-US" xlink:label="lab_kg_MaidenHoldingsLtd.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maiden Holdings, Ltd. [Member]</link:label>
    <link:label id="lab_kg_MaidenHoldingsLtd.Member_documentation_en-US" xlink:label="lab_kg_MaidenHoldingsLtd.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maiden Holdings, Ltd. [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenHoldingsLtd.Member" xlink:href="kg-20260630.xsd#kg_MaidenHoldingsLtd.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MaidenHoldingsLtd.Member" xlink:to="lab_kg_MaidenHoldingsLtd.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019e18df-79c7-7c84-9119-32272bc86885_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurements, Fair Value Hierarchy [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SeidenLPSeidenMGMTLPMember_019e18df-7903-76d8-91a4-b9dda7eac3cf_terseLabel_en-US" xlink:label="lab_kg_SeidenLPSeidenMGMTLPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Seiden LP &amp; Seiden MGMT LP</link:label>
    <link:label id="lab_kg_SeidenLPSeidenMGMTLPMember_label_en-US" xlink:label="lab_kg_SeidenLPSeidenMGMTLPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Seiden LP &amp; Seiden MGMT LP [Member]</link:label>
    <link:label id="lab_kg_SeidenLPSeidenMGMTLPMember_documentation_en-US" xlink:label="lab_kg_SeidenLPSeidenMGMTLPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Seiden LP &amp; Seiden MGMT LP</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeidenLPSeidenMGMTLPMember" xlink:href="kg-20260630.xsd#kg_SeidenLPSeidenMGMTLPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SeidenLPSeidenMGMTLPMember" xlink:to="lab_kg_SeidenLPSeidenMGMTLPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019e18df-79c6-7f8b-9973-d768c9d872dd_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BenefitsLossesAndExpensesNet_019e18df-7903-7806-aec3-8d0e16c47e92_totalLabel_en-US" xlink:label="lab_kg_BenefitsLossesAndExpensesNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total expenses</link:label>
    <link:label id="lab_kg_BenefitsLossesAndExpensesNet_label_en-US" xlink:label="lab_kg_BenefitsLossesAndExpensesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Benefits, Losses and Expenses, Net</link:label>
    <link:label id="lab_kg_BenefitsLossesAndExpensesNet_documentation_en-US" xlink:label="lab_kg_BenefitsLossesAndExpensesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Benefits, Losses and Expenses, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BenefitsLossesAndExpensesNet" xlink:href="kg-20260630.xsd#kg_BenefitsLossesAndExpensesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BenefitsLossesAndExpensesNet" xlink:to="lab_kg_BenefitsLossesAndExpensesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve_019e18df-79c7-76ff-a9a7-758f123f8116_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and loss adjustment expenses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Liability for Claims and Claims Adjustment Expense Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:to="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019e18df-7903-7e54-a6b5-631159a24d72_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss_019e18df-7903-7192-8d4b-42153ec4d9fe_terseLabel_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses of unrealized loss positions</link:label>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss_label_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Continuous Unrealized Loss Position, Accumulated Loss</link:label>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss_documentation_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Continuous Unrealized Loss Position, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:href="kg-20260630.xsd#kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:to="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_019e18df-79c7-7a2d-8b42-f16a9ad01389_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e18df-7a57-7912-9c88-221d9473a23c_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019e18df-7a57-77b1-867a-48aa982b2b87_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_019e18df-7902-7f20-a059-059e3e4c542e_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term to Exit</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Term [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputExpectedTermMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:to="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeDomain_019e18df-7903-7d9e-a093-f29a07610338_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Domain]</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeDomain_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Domain]</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeDomain_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionByTypeDomain" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionByTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionByTypeDomain" xlink:to="lab_kg_RelatedPartyTransactionByTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseExpense_019e18df-79c7-73a9-acd8-845fde24c4fe_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing expense</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseExpense" xlink:to="lab_us-gaap_OperatingLeaseExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss_019e18df-79c7-7669-84bd-a4a74151c6bb_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains recognized for equity securities still held at the reporting date</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:to="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput_019e18df-79c7-7299-8004-00a66bc10665_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities, measurement input</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:to="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_019e18df-79c7-7e85-8efb-58615d1f1295_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, weighted average remaining lease term</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_019e18df-79c7-7638-b3b2-a4a2fa796b45_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable for paid and unpaid claims and claims adjustments, adverse development cover</link:label>
    <link:label id="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_label_en-US" xlink:label="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable For Paid And Unpaid Claims And Claims Adjustments, Adverse Development Cover</link:label>
    <link:label id="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_documentation_en-US" xlink:label="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable For Paid And Unpaid Claims And Claims Adjustments, Adverse Development Cover</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:href="kg-20260630.xsd#kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:to="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_019e18df-79c7-71d6-b0e5-b3cade2f81d3_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Accumulated Loss [Abstract]</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Accumulated Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentMilestoneTypeDomain_019e18df-7a57-7f78-9391-f118b0a26555_terseLabel_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Domain]</link:label>
    <link:label id="lab_kg_InvestmentMilestoneTypeDomain_label_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Domain]</link:label>
    <link:label id="lab_kg_InvestmentMilestoneTypeDomain_documentation_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentMilestoneTypeDomain" xlink:href="kg-20260630.xsd#kg_InvestmentMilestoneTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentMilestoneTypeDomain" xlink:to="lab_kg_InvestmentMilestoneTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementNo.2Member_019e18df-79c7-76e1-a350-c8f3aa82ec20_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 2</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementNo.2Member_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 2 [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementNo.2Member_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementNo.2Member" xlink:href="kg-20260630.xsd#kg_PostTerminationEndorsementNo.2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementNo.2Member" xlink:to="lab_kg_PostTerminationEndorsementNo.2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e18df-7902-79a7-a3fe-5dadd7798291_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (decrease) increase in cash, restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeAxis_019e18df-7903-7efa-b72a-ea8e563bee96_terseLabel_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Axis]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeAxis_label_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Axis]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeAxis_documentation_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:href="kg-20260630.xsd#kg_RestrictedCashAndInvestmentsTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:to="lab_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019e18df-7903-751c-a405-b201b6acc801_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019e18df-7903-7f33-beac-008eb6758815_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019e18df-7903-78f3-af43-6fe9957798dc_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019e18df-79c6-7215-9522-621e15efcf21_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AUMReinsuranceSegmentMember_019e18df-79c7-796a-9956-33136b6b8fbf_terseLabel_en-US" xlink:label="lab_kg_AUMReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AUM Reinsurance Segment</link:label>
    <link:label id="lab_kg_AUMReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_AUMReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AUM Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_AUMReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_AUMReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AUM Reinsurance Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AUMReinsuranceSegmentMember" xlink:href="kg-20260630.xsd#kg_AUMReinsuranceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AUMReinsuranceSegmentMember" xlink:to="lab_kg_AUMReinsuranceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_019e18df-7903-7afa-abc6-69039b8149f5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingActivityByTypeAxis_019fb8af-788f-7d42-b186-a1f454625740_terseLabel_en-US" xlink:label="lab_us-gaap_TradingActivityByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Activity [Axis]</link:label>
    <link:label id="lab_us-gaap_TradingActivityByTypeAxis_label_en-US" xlink:label="lab_us-gaap_TradingActivityByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Activity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingActivityByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TradingActivityByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingActivityByTypeAxis" xlink:to="lab_us-gaap_TradingActivityByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperations_019e18df-79c7-7dd8-9fb8-55877c44d678_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperations_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperations" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ShareRepurchasePlanMember_019e18df-7a58-70ff-a2ee-4f06219ab3e0_terseLabel_en-US" xlink:label="lab_kg_ShareRepurchasePlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Plan</link:label>
    <link:label id="lab_kg_ShareRepurchasePlanMember_label_en-US" xlink:label="lab_kg_ShareRepurchasePlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Plan [Member]</link:label>
    <link:label id="lab_kg_ShareRepurchasePlanMember_documentation_en-US" xlink:label="lab_kg_ShareRepurchasePlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share Repurchase Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ShareRepurchasePlanMember" xlink:href="kg-20260630.xsd#kg_ShareRepurchasePlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ShareRepurchasePlanMember" xlink:to="lab_kg_ShareRepurchasePlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceDisclosuresAbstract_019e18df-7a58-73df-84a3-b33eb891e7db_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_ReinsuranceDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_ReinsuranceDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceDisclosuresAbstract" xlink:to="lab_us-gaap_ReinsuranceDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_019e18df-7a57-7149-a4f8-b77eeec3fc06_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_019e18df-7a57-7ecc-94e3-303bdf214851_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums and losses related to policies, percentage</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Premiums and Losses Related to Policies</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Premiums and Losses Related to Policies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:to="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019e18df-7903-75ec-88d9-4cd185061158_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_019e18df-79c7-7cdd-a5f1-1ad73c39890b_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, percentage of required funding on obligations</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percentage Of Required Funding On Obligations</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percentage Of Required Funding On Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:to="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededPremiumsEarned_019e18df-7902-7b05-b4c2-df1aa17f2165_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CededPremiumsEarned" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Ceded</link:label>
    <link:label id="lab_us-gaap_CededPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_CededPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ceded Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CededPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededPremiumsEarned" xlink:to="lab_us-gaap_CededPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019e18df-7902-72f4-a781-4d27214b764c_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019e18df-79c6-75ab-942b-dbc2d3de1934_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares ($0.01 par value; 2026: 10,108,600 and 2025: 9,979,477 shares issued; 2026: 7,824,030 and 2025: 7,741,943 shares outstanding)</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019e18df-7903-756d-a7e5-e15c937d7da8_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
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    <link:label id="lab_us-gaap_DepreciationAmortizationAndAccretionNet_019e18df-7903-75bf-8917-e50d872bf6e6_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-cash (income) expenses including credit losses, depreciation, amortization, leases</link:label>
    <link:label id="lab_us-gaap_DepreciationAmortizationAndAccretionNet_label_en-US" xlink:label="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Amortization and Accretion, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationAmortizationAndAccretionNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:to="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock_019e18df-7902-7b48-ada4-0077eb9f5253_negatedTerseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Equity portion of consideration transferred to Maiden Reinsurance</link:label>
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    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest in Treasury Stock</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_019e18df-79c7-77eb-be52-02aee2880ece_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Issuances of Senior Notes Outstanding</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
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    <link:label id="lab_kg_KILHMember_019e18df-7903-719e-aa53-8052d7282efd_terseLabel_en-US" xlink:label="lab_kg_KILHMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">KILH</link:label>
    <link:label id="lab_kg_KILHMember_label_en-US" xlink:label="lab_kg_KILHMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">KILH [Member]</link:label>
    <link:label id="lab_kg_KILHMember_documentation_en-US" xlink:label="lab_kg_KILHMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">KILH</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KILHMember" xlink:href="kg-20260630.xsd#kg_KILHMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KILHMember" xlink:to="lab_kg_KILHMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
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    <link:label id="lab_kg_RestrictedStockAndPerformanceSharesMember_019fd8f8-bd28-7f68-a9c8-9bc7d0a463e1_terseLabel_en-US" xlink:label="lab_kg_RestrictedStockAndPerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock and Performance Shares</link:label>
    <link:label id="lab_kg_RestrictedStockAndPerformanceSharesMember_label_en-US" xlink:label="lab_kg_RestrictedStockAndPerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock and Performance Shares [Member]</link:label>
    <link:label id="lab_kg_RestrictedStockAndPerformanceSharesMember_documentation_en-US" xlink:label="lab_kg_RestrictedStockAndPerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Stock and Performance Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedStockAndPerformanceSharesMember" xlink:href="kg-20260630.xsd#kg_RestrictedStockAndPerformanceSharesMember"/>
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    <link:label id="lab_dei_AmendmentFlag_019e18df-7a58-7275-a573-1673b642e9fc_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments_019e18df-7a57-7d09-b83b-e52a6dfb2fdb_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale and redemption of equity method investments</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfEquityMethodInvestments"/>
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    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_019e18df-7903-7d8f-a5f5-c7b22a394bc5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, FV-NI [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, FV-NI [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems"/>
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    <link:label id="lab_kg_AllowanceForCreditLossPeriodIncreaseDecrease_019e18df-7a58-737a-921e-a86778a376e8_terseLabel_en-US" xlink:label="lab_kg_AllowanceForCreditLossPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation expense</link:label>
    <link:label id="lab_kg_AllowanceForCreditLossPeriodIncreaseDecrease_label_en-US" xlink:label="lab_kg_AllowanceForCreditLossPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Period Increase (Decrease)</link:label>
    <link:label id="lab_kg_AllowanceForCreditLossPeriodIncreaseDecrease_documentation_en-US" xlink:label="lab_kg_AllowanceForCreditLossPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AllowanceForCreditLossPeriodIncreaseDecrease" xlink:href="kg-20260630.xsd#kg_AllowanceForCreditLossPeriodIncreaseDecrease"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent_019e18df-7a57-725b-a0da-b594e3590ad9_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, before Tax, Portion Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract_019e18df-7903-783a-afa3-60905e1540c3_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss and LAE</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Net [Abstract]</link:label>
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    <link:label id="lab_kg_InterestAndAmortizationExpensesNet_label_en-US" xlink:label="lab_kg_InterestAndAmortizationExpensesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Amortization Expenses, Net</link:label>
    <link:label id="lab_kg_InterestAndAmortizationExpensesNet_documentation_en-US" xlink:label="lab_kg_InterestAndAmortizationExpensesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest and Amortization Expenses, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InterestAndAmortizationExpensesNet" xlink:href="kg-20260630.xsd#kg_InterestAndAmortizationExpensesNet"/>
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    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_019e18df-7903-71ca-a819-27404fdc92ff_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross unrealized losses</link:label>
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    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_019e18df-7a58-7de8-b09a-0cded1c25643_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:href="kg-20260630.xsd#kg_OtherInvestmentsAndEquityMethodInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:to="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue_019e18df-7a57-7e10-b083-aed7be970db3_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">12 Months or More</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Twelve Months or Longer, Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Twelve Months or Longer, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_019e18df-7903-7ab4-945f-bfd54b6a3c9c_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued on Combination Agreement</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_019e18df-79c7-7d72-a380-0fd3f98d3110_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired Level 3 investments</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Transfers Into Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss_019e18df-7903-7b54-b263-ab2f69397731_negatedTotalLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Accumulated Loss</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_019e18df-79c7-7c56-aba5-412329bcc5c2_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsInDirectLendingEntitiesMember_019e18df-79c7-722c-bd22-957b4b8a823c_terseLabel_en-US" xlink:label="lab_kg_InvestmentsInDirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment in direct lending entities</link:label>
    <link:label id="lab_kg_InvestmentsInDirectLendingEntitiesMember_label_en-US" xlink:label="lab_kg_InvestmentsInDirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments In Direct Lending Entities [Member]</link:label>
    <link:label id="lab_kg_InvestmentsInDirectLendingEntitiesMember_documentation_en-US" xlink:label="lab_kg_InvestmentsInDirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments In Direct Lending Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsInDirectLendingEntitiesMember" xlink:href="kg-20260630.xsd#kg_InvestmentsInDirectLendingEntitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsInDirectLendingEntitiesMember" xlink:to="lab_kg_InvestmentsInDirectLendingEntitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019e18df-79c7-7a41-b619-52843a3386f2_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ShareRepurchaseProgramDomain_019e18df-79c7-76b8-81e6-e53401c9633b_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Domain]</link:label>
    <link:label id="lab_srt_ShareRepurchaseProgramDomain_label_en-US" xlink:label="lab_srt_ShareRepurchaseProgramDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ShareRepurchaseProgramDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ShareRepurchaseProgramDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ShareRepurchaseProgramDomain" xlink:to="lab_srt_ShareRepurchaseProgramDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019e18df-79c7-7d1a-813d-18d65189ce13_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares - basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019e18df-79c7-7213-a10e-6b22fd7aff78_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares &#8211;&#160;basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FairValueDiscountOnAcquiredReservesMember_019e18df-7903-7e7a-ad96-54e1420143f5_verboseLabel_en-US" xlink:label="lab_kg_FairValueDiscountOnAcquiredReservesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value discount on net reserves acquired</link:label>
    <link:label id="lab_kg_FairValueDiscountOnAcquiredReservesMember_019e18df-7903-74a2-91f3-740f885ed6c9_terseLabel_en-US" xlink:label="lab_kg_FairValueDiscountOnAcquiredReservesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense: fair value discount on net reserves acquired</link:label>
    <link:label id="lab_kg_FairValueDiscountOnAcquiredReservesMember_label_en-US" xlink:label="lab_kg_FairValueDiscountOnAcquiredReservesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Discount on Acquired Reserves [Member]</link:label>
    <link:label id="lab_kg_FairValueDiscountOnAcquiredReservesMember_documentation_en-US" xlink:label="lab_kg_FairValueDiscountOnAcquiredReservesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Discount on Acquired Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FairValueDiscountOnAcquiredReservesMember" xlink:href="kg-20260630.xsd#kg_FairValueDiscountOnAcquiredReservesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FairValueDiscountOnAcquiredReservesMember" xlink:to="lab_kg_FairValueDiscountOnAcquiredReservesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_019e18df-7a57-7571-b5f6-1a7f50eae262_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Quota Share Arrangements with AmTrust</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectPremiumsEarned_019e18df-79c7-7bab-9ed2-05988f4d5419_terseLabel_en-US" xlink:label="lab_us-gaap_DirectPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct</link:label>
    <link:label id="lab_us-gaap_DirectPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_DirectPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DirectPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectPremiumsEarned" xlink:to="lab_us-gaap_DirectPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember_019e18df-7903-7ef8-9e7a-edc925d4a5dd_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Maximum Loss Corridor</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Maximum Loss Corridor [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Maximum Loss Corridor [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:href="kg-20260630.xsd#kg_PostTerminationEndorsementMaximumLossCorridorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:to="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019e18df-79c7-759c-bad4-30659348ca14_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsAbstract_019e18df-79c7-7ec5-a750-b5935cef0dec_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Abstract]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsAbstract" xlink:to="lab_us-gaap_ScheduleOfInvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_019e18df-7903-793d-a1f7-fe11f07b7f9d_terseLabel_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets, valued by third party, percentage</link:label>
    <link:label id="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_label_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure, Valued by Third Party, Percentage</link:label>
    <link:label id="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_documentation_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure, Valued by Third Party, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:href="kg-20260630.xsd#kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:to="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsAbstract_019e18df-79c7-7958-89dc-42e46ed31319_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments:</link:label>
    <link:label id="lab_us-gaap_InvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsAbstract" xlink:to="lab_us-gaap_InvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019e18df-79c7-7368-823b-6e06dc961309_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_019e18df-79c6-7141-a56f-b03aa329ce3a_negatedLabel_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange and other (gains) losses</link:label>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_019e18df-79c6-740c-8067-1f23bc6fe106_negatedTerseLabel_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange and other (gains) losses</link:label>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_019e18df-79c6-7d5e-9a49-f0d2d10eeb5c_terseLabel_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange and other gains, net</link:label>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_label_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Transaction and Other Gain (Loss), before Tax</link:label>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_documentation_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Foreign Currency Transaction and Other Gain (Loss), before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:href="kg-20260630.xsd#kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:to="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_019e18df-7a57-7d5c-aa1c-d3138e97a037_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput_019e18df-7a57-79e2-8705-5b2db714da0d_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Receivable, measurement inputs</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput_label_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Asset, Measurement Input</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput_documentation_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Asset, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:href="kg-20260630.xsd#kg_BusinessCombinationContingentConsiderationAssetMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:to="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019e18df-79c7-756c-9f74-09e94554e05b_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_019e18df-7a58-7f48-a480-6b18c5f09bcf_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Original fair value adjustment at acquisition date</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFinanceCostsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsGross" xlink:to="lab_us-gaap_DeferredFinanceCostsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019e18df-7903-718f-8e99-d4c91b13cc15_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income attributable to Kestrel common shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ProgramServicesSegmentMember_019e18df-7903-7f30-937b-0a6d4be3f4de_terseLabel_en-US" xlink:label="lab_kg_ProgramServicesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Program Services</link:label>
    <link:label id="lab_kg_ProgramServicesSegmentMember_label_en-US" xlink:label="lab_kg_ProgramServicesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Program Services Segment [Member]</link:label>
    <link:label id="lab_kg_ProgramServicesSegmentMember_documentation_en-US" xlink:label="lab_kg_ProgramServicesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Program Services Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ProgramServicesSegmentMember" xlink:href="kg-20260630.xsd#kg_ProgramServicesSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ProgramServicesSegmentMember" xlink:to="lab_kg_ProgramServicesSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves_019e18df-7903-722a-8c47-b78c8f77c8ac_terseLabel_en-US" xlink:label="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative arrangement, payment of commuted reserves</link:label>
    <link:label id="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves_label_en-US" xlink:label="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Payment of Commuted Reserves</link:label>
    <link:label id="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves_documentation_en-US" xlink:label="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Payment of Commuted Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:href="kg-20260630.xsd#kg_CollaborativeArrangementPaymentOfCommutedReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:to="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_019e18df-79c7-743f-8fd1-63f2033cc786_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_019e18df-79c7-720d-ba2c-fe43b88300d2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember_019e18df-79c7-766b-be68-231e61ddee71_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBITDA &amp; Commission Discount Rate</link:label>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember_label_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA and Commission Discount Rate [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA and Commission Discount Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:href="kg-20260630.xsd#kg_MeasurementInputEBITDAAndCommissionDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:to="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_019e18df-7a58-7735-a781-780168220929_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected credit losses on acquired recoverables under the Combination</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:to="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain_019e18df-7902-76a2-84fe-a8a6e568c3ae_terseLabel_en-US" xlink:label="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities, gross gains</link:label>
    <link:label id="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain_label_en-US" xlink:label="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized And Unrealized Gain</link:label>
    <link:label id="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain_documentation_en-US" xlink:label="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized And Unrealized Gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:href="kg-20260630.xsd#kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:to="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_019e18df-79c7-7e66-a770-41f71b96f4ad_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Reinsurance Recoverable on Unpaid Losses</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Reinsurance Recoverable on Unpaid Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_019e18df-79c7-7218-90fa-b54a3015e207_negatedLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Investment expenses</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Investment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInvestmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:to="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019e18df-7a57-7fb9-b8a8-c31963c253de_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recently Adopted Accounting Standards and Recently Issued Accounting Standards Not Yet Adopted</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_LitigationCaseAxis_019e18df-7a58-75b4-ae25-fe09138ec66e_terseLabel_en-US" xlink:label="lab_srt_LitigationCaseAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Case [Axis]</link:label>
    <link:label id="lab_srt_LitigationCaseAxis_label_en-US" xlink:label="lab_srt_LitigationCaseAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Case [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_LitigationCaseAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_LitigationCaseAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_LitigationCaseAxis" xlink:to="lab_srt_LitigationCaseAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019e18df-79c7-747d-ac8e-f2ed74ae5a14_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization for the fair value adjustment</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsOriginalOrAmortizedCostBasis_019e18df-7a57-77b2-a75d-fc4941e503fe_terseLabel_en-US" xlink:label="lab_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_kg_InvestmentsOriginalOrAmortizedCostBasis_label_en-US" xlink:label="lab_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Original or Amortized Cost Basis</link:label>
    <link:label id="lab_kg_InvestmentsOriginalOrAmortizedCostBasis_documentation_en-US" xlink:label="lab_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Original or Amortized Cost Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:href="kg-20260630.xsd#kg_InvestmentsOriginalOrAmortizedCostBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:to="lab_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsFairValueOptionMember_019e18df-7a57-77cd-bd9d-f726a68dc282_terseLabel_en-US" xlink:label="lab_kg_InvestmentsFairValueOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total equity method investments with fair value option</link:label>
    <link:label id="lab_kg_InvestmentsFairValueOptionMember_label_en-US" xlink:label="lab_kg_InvestmentsFairValueOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Fair Value Option [Member]</link:label>
    <link:label id="lab_kg_InvestmentsFairValueOptionMember_documentation_en-US" xlink:label="lab_kg_InvestmentsFairValueOptionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Fair Value Option</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsFairValueOptionMember" xlink:href="kg-20260630.xsd#kg_InvestmentsFairValueOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsFairValueOptionMember" xlink:to="lab_kg_InvestmentsFairValueOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_019e18df-7903-78ba-8e5f-7463b6c63c99_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019e18df-7a57-7062-b9fc-977cc1840ac3_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Senior notes, net</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019e18df-7a57-7dc5-b5a8-76b3cca733f2_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying value</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesFairValue_019e18df-79c7-7505-922a-83142a233a27_verboseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_kg_FixedMaturitiesFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesFairValue" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesFairValue" xlink:to="lab_kg_FixedMaturitiesFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e18df-79c6-7ef0-83f2-ae86c2687b58_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019e18df-7903-7bc4-95f5-507d92ead316_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member_019e18df-79c7-7cf5-ae3f-864870f72094_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investments - preferred shares 3</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 3 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:href="kg-20260630.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019e18df-79c7-7727-bcaf-618b6081e1be_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ThirdPartyAgreementsMember_019e18df-7a57-74e9-bc1a-0cfeec0c3d8a_terseLabel_en-US" xlink:label="lab_kg_ThirdPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third Party Agreements</link:label>
    <link:label id="lab_kg_ThirdPartyAgreementsMember_label_en-US" xlink:label="lab_kg_ThirdPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Agreements [Member]</link:label>
    <link:label id="lab_kg_ThirdPartyAgreementsMember_documentation_en-US" xlink:label="lab_kg_ThirdPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third Party Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ThirdPartyAgreementsMember" xlink:href="kg-20260630.xsd#kg_ThirdPartyAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ThirdPartyAgreementsMember" xlink:to="lab_kg_ThirdPartyAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsWrittenGross_019e18df-7a57-7d9f-8e1a-f97dc02dea69_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenGross_019e18df-7a57-7bfa-97fb-3c0a5af70e26_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenGross" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenGross_label_en-US" xlink:label="lab_us-gaap_PremiumsWrittenGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PremiumsWrittenGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsWrittenGross" xlink:to="lab_us-gaap_PremiumsWrittenGross" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceCollateralByThirdParty_019e18df-7903-7ac7-a5a2-0cb932d763d1_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceCollateralByThirdParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral by third party</link:label>
    <link:label id="lab_kg_ReinsuranceCollateralByThirdParty_label_en-US" xlink:label="lab_kg_ReinsuranceCollateralByThirdParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Collateral By Third Party</link:label>
    <link:label id="lab_kg_ReinsuranceCollateralByThirdParty_documentation_en-US" xlink:label="lab_kg_ReinsuranceCollateralByThirdParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance, Collateral By Third Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceCollateralByThirdParty" xlink:href="kg-20260630.xsd#kg_ReinsuranceCollateralByThirdParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceCollateralByThirdParty" xlink:to="lab_kg_ReinsuranceCollateralByThirdParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019e18df-79c7-7b1f-b9cd-50f4218ed335_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesReceivableGross_019e18e2-02a8-7205-9a82-daa279aeffb5_terseLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loan receivable from related party</link:label>
    <link:label id="lab_us-gaap_NotesReceivableGross_label_en-US" xlink:label="lab_us-gaap_NotesReceivableGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesReceivableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesReceivableGross" xlink:to="lab_us-gaap_NotesReceivableGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireMarketableSecurities_019e18df-79c7-7e0e-9ea5-9d3919ec9acd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of fixed maturities&#160;</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireMarketableSecurities_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireMarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:to="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_019e18df-7a57-74af-8c24-c9ca0f7e197c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares issuable under incentive plans (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrent_019e18df-7903-7f6d-adfd-2371dc8790b2_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrent" xlink:to="lab_us-gaap_InterestPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_019e18df-7903-7a85-909e-5e2b242b5136_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasuryBondSecuritiesMember_019e18df-79c7-7c95-b138-d976bbfb49fd_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasuryBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. treasury bills</link:label>
    <link:label id="lab_us-gaap_USTreasuryBondSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasuryBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Bond Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryBondSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_USTreasuryBondSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasuryBondSecuritiesMember" xlink:to="lab_us-gaap_USTreasuryBondSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyAgreementsMember_019e18df-79c7-70ea-9917-a39588103d54_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Agreements</link:label>
    <link:label id="lab_kg_RelatedPartyAgreementsMember_label_en-US" xlink:label="lab_kg_RelatedPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Agreements [Member]</link:label>
    <link:label id="lab_kg_RelatedPartyAgreementsMember_documentation_en-US" xlink:label="lab_kg_RelatedPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyAgreementsMember" xlink:href="kg-20260630.xsd#kg_RelatedPartyAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyAgreementsMember" xlink:to="lab_kg_RelatedPartyAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_019e18df-7903-7079-b2b3-a1c7998edb8d_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denominator:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsTable_019e18df-7903-7b79-8604-344386a191e6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ExtellHudsonWaterfrontHoldingsMember_019e18df-7903-757f-8cdf-2184990f46bf_terseLabel_en-US" xlink:label="lab_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extell Hudson Waterfront Holdings</link:label>
    <link:label id="lab_kg_ExtellHudsonWaterfrontHoldingsMember_label_en-US" xlink:label="lab_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extell Hudson Waterfront Holdings [Member]</link:label>
    <link:label id="lab_kg_ExtellHudsonWaterfrontHoldingsMember_documentation_en-US" xlink:label="lab_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Extell Hudson Waterfront Holdings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:href="kg-20260630.xsd#kg_ExtellHudsonWaterfrontHoldingsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:to="lab_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_019e18df-79c7-7059-a54b-015decec5b2f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of other investments</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireOtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019e18df-7902-769a-9236-fad80f905763_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior notes - principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019e18df-7902-7c34-9cd2-af020321dc96_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_019e18df-79c6-7b86-a2cd-3d6518020fd1_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterestAndDividend_019e18df-7903-7138-a337-f9c123b333aa_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterestAndDividend" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterestAndDividend_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterestAndDividend" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest and Dividend</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterestAndDividend" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterestAndDividend"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterestAndDividend" xlink:to="lab_us-gaap_InvestmentIncomeInterestAndDividend" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e18df-79c6-7068-b443-e0cf9df893b6_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares - diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e18df-79c6-7086-9e01-bce05d75705f_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares - diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019e18df-79c6-7513-998a-45c17793ffe7_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_019e18df-79c7-7ef7-9122-fe155a453746_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SeniorNotes2016Member_019e18df-79c7-7800-974a-9b2e467b1699_verboseLabel_en-US" xlink:label="lab_kg_SeniorNotes2016Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes - MHLA &#8211; 6.625%</link:label>
    <link:label id="lab_kg_SeniorNotes2016Member_019e18df-79c7-738f-bd6d-a9c4977f3537_terseLabel_en-US" xlink:label="lab_kg_SeniorNotes2016Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2016 Senior Notes</link:label>
    <link:label id="lab_kg_SeniorNotes2016Member_label_en-US" xlink:label="lab_kg_SeniorNotes2016Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes 2016 [Member]</link:label>
    <link:label id="lab_kg_SeniorNotes2016Member_documentation_en-US" xlink:label="lab_kg_SeniorNotes2016Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes 2016 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2016Member" xlink:href="kg-20260630.xsd#kg_SeniorNotes2016Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SeniorNotes2016Member" xlink:to="lab_kg_SeniorNotes2016Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_019e18df-79c7-76f1-8bdf-a61a2e041f44_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_019e18df-7a57-767a-bc78-59c7faf46b0c_terseLabel_en-US" xlink:label="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior notice to be given before redemption date</link:label>
    <link:label id="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_label_en-US" xlink:label="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Prior Notice, Redemption Period, Start Date</link:label>
    <link:label id="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_documentation_en-US" xlink:label="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Prior Notice, Redemption Period, Start Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:href="kg-20260630.xsd#kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:to="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockNumberOfVotesPerShare_019e18df-7a58-7bcc-b5a2-58f13a2ab4bb_terseLabel_en-US" xlink:label="lab_kg_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of votes per share</link:label>
    <link:label id="lab_kg_CommonStockNumberOfVotesPerShare_label_en-US" xlink:label="lab_kg_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Number Of Votes Per Share</link:label>
    <link:label id="lab_kg_CommonStockNumberOfVotesPerShare_documentation_en-US" xlink:label="lab_kg_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Number Of Votes Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockNumberOfVotesPerShare" xlink:href="kg-20260630.xsd#kg_CommonStockNumberOfVotesPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommonStockNumberOfVotesPerShare" xlink:to="lab_kg_CommonStockNumberOfVotesPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedInvestmentIncomeReceivable_019e18df-7903-7b86-8aaf-7939a56fb140_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued investment income</link:label>
    <link:label id="lab_us-gaap_AccruedInvestmentIncomeReceivable_label_en-US" xlink:label="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Investment Income Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedInvestmentIncomeReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedInvestmentIncomeReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedInvestmentIncomeReceivable" xlink:to="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_019e18df-79c6-7173-81d6-6282ada5ffc2_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury shares</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_OperatingLeaseEscalatingFeePercentage_019e18df-7903-79a1-97ef-449ed1aadedf_terseLabel_en-US" xlink:label="lab_kg_OperatingLeaseEscalatingFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease payments to escalating fee, percentage</link:label>
    <link:label id="lab_kg_OperatingLeaseEscalatingFeePercentage_label_en-US" xlink:label="lab_kg_OperatingLeaseEscalatingFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Escalating Fee Percentage</link:label>
    <link:label id="lab_kg_OperatingLeaseEscalatingFeePercentage_documentation_en-US" xlink:label="lab_kg_OperatingLeaseEscalatingFeePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Lease, Escalating Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OperatingLeaseEscalatingFeePercentage" xlink:href="kg-20260630.xsd#kg_OperatingLeaseEscalatingFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OperatingLeaseEscalatingFeePercentage" xlink:to="lab_kg_OperatingLeaseEscalatingFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_019e18df-7a57-7621-ae79-93f62fe8579d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AUMFinancialServicesInc.Member_019e18df-79c7-7fca-8676-7b543b9ab8af_terseLabel_en-US" xlink:label="lab_kg_AUMFinancialServicesInc.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AUM Financial Services, Inc.</link:label>
    <link:label id="lab_kg_AUMFinancialServicesInc.Member_label_en-US" xlink:label="lab_kg_AUMFinancialServicesInc.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AUM Financial Services, Inc. [Member]</link:label>
    <link:label id="lab_kg_AUMFinancialServicesInc.Member_documentation_en-US" xlink:label="lab_kg_AUMFinancialServicesInc.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AUM Programs Financial Services, Inc.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AUMFinancialServicesInc.Member" xlink:href="kg-20260630.xsd#kg_AUMFinancialServicesInc.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AUMFinancialServicesInc.Member" xlink:to="lab_kg_AUMFinancialServicesInc.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_WeightedAverageAmortizationPeriodAbstract_019e18df-79c7-7a54-9361-50754bd2bbab_terseLabel_en-US" xlink:label="lab_kg_WeightedAverageAmortizationPeriodAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Amortization Period</link:label>
    <link:label id="lab_kg_WeightedAverageAmortizationPeriodAbstract_label_en-US" xlink:label="lab_kg_WeightedAverageAmortizationPeriodAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Amortization Period [Abstract]</link:label>
    <link:label id="lab_kg_WeightedAverageAmortizationPeriodAbstract_documentation_en-US" xlink:label="lab_kg_WeightedAverageAmortizationPeriodAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_WeightedAverageAmortizationPeriodAbstract" xlink:href="kg-20260630.xsd#kg_WeightedAverageAmortizationPeriodAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_WeightedAverageAmortizationPeriodAbstract" xlink:to="lab_kg_WeightedAverageAmortizationPeriodAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_019e18df-7903-783e-b2fa-e304b1bc8810_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputCapRateMember_019e18df-79c7-7c68-9410-d7fa746566cb_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputCapRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exit Cap Rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputCapRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputCapRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Cap Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputCapRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputCapRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputCapRateMember" xlink:to="lab_us-gaap_MeasurementInputCapRateMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_OtherCommitmentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsTableTextBlock" xlink:to="lab_us-gaap_OtherCommitmentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelGroupLtd.Member_019e18df-7903-7f5d-8399-1a7eafcd0b55_terseLabel_en-US" xlink:label="lab_kg_KestrelGroupLtd.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group, Ltd.</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelGroupLtd.Member" xlink:to="lab_kg_KestrelGroupLtd.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019e18df-7a58-77b4-acf5-a8f7198ebc9c_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
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    <link:label id="lab_us-gaap_RestrictedInvestments_019e18df-7903-7f90-bac8-e24e9e17d669_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted investments</link:label>
    <link:label id="lab_us-gaap_RestrictedInvestments_label_en-US" xlink:label="lab_us-gaap_RestrictedInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedInvestments" xlink:to="lab_us-gaap_RestrictedInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders_019e18df-7903-7ffa-a9c8-6d0389410c2c_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash consideration paid to shareholders at Closing for fractional shares</link:label>
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    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Cash Consideration Paid To Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:href="kg-20260630.xsd#kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders"/>
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    <link:label id="lab_us-gaap_AlternativeInvestmentMeasurementInput_019e18df-79c7-7eb9-8c76-3a137b9276d6_terseLabel_en-US" xlink:label="lab_us-gaap_AlternativeInvestmentMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Investments, measurement inputs</link:label>
    <link:label id="lab_us-gaap_AlternativeInvestmentMeasurementInput_label_en-US" xlink:label="lab_us-gaap_AlternativeInvestmentMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Alternative Investment, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestmentMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AlternativeInvestmentMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AlternativeInvestmentMeasurementInput" xlink:to="lab_us-gaap_AlternativeInvestmentMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate_019e18df-79c7-71e1-8860-01c637ba46e4_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective yield</link:label>
    <link:label id="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate_label_en-US" xlink:label="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable with Imputed Interest, Effective Yield (Interest Rate)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate"/>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019e18df-7903-777e-89b3-3db09dfd201a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Elements Used in Calculating Basic and Diluted Earnings Per Common Share</link:label>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_019e18df-79c7-7fce-be10-319c339d6a0b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
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    <link:label id="lab_srt_MinimumMember_019e18df-79c7-71e5-bf49-2c3740f74003_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_019e18df-79c7-742e-aed9-f6bb94807e24_verboseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Low</link:label>
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    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member_019e18df-79c7-7187-9e71-ac203db66a5d_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investments - preferred shares 2</link:label>
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    <link:label id="lab_us-gaap_InvestmentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_InvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Fair Value Disclosure</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAbstract_019e18df-7903-7a1f-afcb-b1cfbb79fc44_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e18df-7a57-7b7e-9c5a-9ee511459097_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of exchange rate changes on foreign currency cash, restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_019e18df-7903-793b-8637-980724ad6601_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeLocationBalanceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:to="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainContingenciesTable_019e18df-79c6-75b1-bbcb-55ead190d98d_terseLabel_en-US" xlink:label="lab_us-gaap_GainContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_GainContingenciesTable_label_en-US" xlink:label="lab_us-gaap_GainContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainContingenciesTable" xlink:to="lab_us-gaap_GainContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_019e18df-7902-77c9-a63b-4beb852514c7_verboseLabel_en-US" xlink:label="lab_kg_ValueOfBusinessAcquiredMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Value of Business Acquired</link:label>
    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_019e18df-7902-74d2-adfd-1cc3b3f63c2e_terseLabel_en-US" xlink:label="lab_kg_ValueOfBusinessAcquiredMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense: VOBA</link:label>
    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_label_en-US" xlink:label="lab_kg_ValueOfBusinessAcquiredMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Value of Business Acquired [Member]</link:label>
    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_documentation_en-US" xlink:label="lab_kg_ValueOfBusinessAcquiredMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Value of Business Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ValueOfBusinessAcquiredMember" xlink:href="kg-20260630.xsd#kg_ValueOfBusinessAcquiredMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ValueOfBusinessAcquiredMember" xlink:to="lab_kg_ValueOfBusinessAcquiredMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_019e18df-79c7-75cd-8224-b5ab7ed94c2d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Senior Notes</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Liabilities Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BarryZyskindMember_019e18df-7903-78d1-ae2f-bac95142a6f7_terseLabel_en-US" xlink:label="lab_kg_BarryZyskindMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Barry Zyskind</link:label>
    <link:label id="lab_kg_BarryZyskindMember_label_en-US" xlink:label="lab_kg_BarryZyskindMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Barry Zyskind [Member]</link:label>
    <link:label id="lab_kg_BarryZyskindMember_documentation_en-US" xlink:label="lab_kg_BarryZyskindMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Barry Zyskind</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BarryZyskindMember" xlink:href="kg-20260630.xsd#kg_BarryZyskindMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BarryZyskindMember" xlink:to="lab_kg_BarryZyskindMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_019e18df-7903-71df-8489-fb4e47452eb0_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019e18df-7903-771e-8b4c-cfde0d1b0651_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Authorized share capital (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember_019e18df-7a57-70e9-a535-ec52fdf275cc_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Duration matched discount rates &amp; arbitration decision</link:label>
    <link:label id="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember_label_en-US" xlink:label="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Duration Matched Discount Rates [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Duration Matched Discount Rates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:href="kg-20260630.xsd#kg_MeasurementInputDurationMatchedDiscountRatesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:to="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_019e18df-79c6-7ee2-8a7a-b6185f165e7b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain_019e18df-79c7-7883-8691-ad310f933187_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, gross gains</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember_019e18df-79c7-7b97-8ae7-8544d2e7bc4c_terseLabel_en-US" xlink:label="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share Reinsurance Segment</link:label>
    <link:label id="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share Reinsurance Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:href="kg-20260630.xsd#kg_AmtrustQuotaShareReinsuranceSegmentMember"/>
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    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_019e18df-7903-727c-9b35-a8e3859528e4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019e18df-7903-7dbb-aae9-7b4a0d1cd2e9_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_019e18df-79c7-7d5c-9b47-5e587a8d6c64_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
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    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_019e18df-79c7-7206-b912-fbb17d3635e9_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_019e18df-7903-7ce7-9a5f-f60b7c0cbe2b_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity securities: at fair value (Cost: 2026: $11,145; 2025: $11,145)</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_019e18df-7903-7721-b2eb-0ee72b653836_netLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_019e18df-7903-7482-bb97-8ae2056cee55_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNi" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNi"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNi" xlink:to="lab_us-gaap_EquitySecuritiesFvNi" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectPremiumsWritten_019e18df-79c6-7740-881d-5ac245dd4b62_terseLabel_en-US" xlink:label="lab_us-gaap_DirectPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct</link:label>
    <link:label id="lab_us-gaap_DirectPremiumsWritten_label_en-US" xlink:label="lab_us-gaap_DirectPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Premiums Written</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectPremiumsWritten" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DirectPremiumsWritten"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectPremiumsWritten" xlink:to="lab_us-gaap_DirectPremiumsWritten" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_019e18df-7a57-7c85-8676-6f0db1d2ca8c_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019e18df-79c7-73bd-84e3-50f9422d10c3_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, liability</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019e18df-79c7-7c3e-b20f-f6f1381d16fa_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total discounted operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments_019e18df-79c7-78c7-8034-e8c12fa86c74_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale and redemption of other investments</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale and Maturity of Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments" xlink:to="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AssetPurchaseAgreementMember_019e18df-7902-76ec-9f17-59b662420dae_terseLabel_en-US" xlink:label="lab_kg_AssetPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Purchase Agreement</link:label>
    <link:label id="lab_kg_AssetPurchaseAgreementMember_label_en-US" xlink:label="lab_kg_AssetPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Purchase Agreement [Member]</link:label>
    <link:label id="lab_kg_AssetPurchaseAgreementMember_documentation_en-US" xlink:label="lab_kg_AssetPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Purchase Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetPurchaseAgreementMember" xlink:href="kg-20260630.xsd#kg_AssetPurchaseAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AssetPurchaseAgreementMember" xlink:to="lab_kg_AssetPurchaseAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1_019e18df-79c7-7e3e-bea1-4711ae2340cd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net paid losses related to Current year</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Claims Paid, Current Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:to="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_019e18df-79c7-75b4-9524-23dc468c11cf_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LPTADCAgreementMember_019e18df-7a57-7490-a27e-dc988b040752_terseLabel_en-US" xlink:label="lab_kg_LPTADCAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LPT/ADC Agreement</link:label>
    <link:label id="lab_kg_LPTADCAgreementMember_label_en-US" xlink:label="lab_kg_LPTADCAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">LPT/ADC Agreement [Member]</link:label>
    <link:label id="lab_kg_LPTADCAgreementMember_documentation_en-US" xlink:label="lab_kg_LPTADCAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">LPT/ADC Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LPTADCAgreementMember" xlink:href="kg-20260630.xsd#kg_LPTADCAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LPTADCAgreementMember" xlink:to="lab_kg_LPTADCAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_019e18df-7903-791c-a525-aae1f3977b64_verboseLabel_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Reinsurance</link:label>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_019e18df-7903-72d0-a471-8ca3295320b5_terseLabel_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Reinsurance legacy business</link:label>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Reinsurance Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustReinsuranceSegmentMember" xlink:href="kg-20260630.xsd#kg_AmTrustReinsuranceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustReinsuranceSegmentMember" xlink:to="lab_kg_AmTrustReinsuranceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019e18df-79c7-77c1-a5bc-4fd19da4b4f1_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments, Contingencies and Guarantees</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_019e18df-7903-7b25-97b3-f652f00bb74e_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract_019e18df-79c6-78f0-ba36-e54810ae1122_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract_label_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenNetConsolidatedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PremiumsWrittenNetConsolidatedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsWrittenNetConsolidatedAbstract" xlink:to="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_019e18df-7902-7fb4-8a85-96bcde088597_verboseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Corporate assets</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_019e18df-79c7-7727-9a87-f85cafa997a2_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAxis" xlink:to="lab_us-gaap_BusinessAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MaidenReinsuranceMember_019e18df-7902-778a-87a0-465cf23197b8_terseLabel_en-US" xlink:label="lab_kg_MaidenReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maiden Reinsurance</link:label>
    <link:label id="lab_kg_MaidenReinsuranceMember_label_en-US" xlink:label="lab_kg_MaidenReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maiden Reinsurance [Member]</link:label>
    <link:label id="lab_kg_MaidenReinsuranceMember_documentation_en-US" xlink:label="lab_kg_MaidenReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maiden Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenReinsuranceMember" xlink:href="kg-20260630.xsd#kg_MaidenReinsuranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MaidenReinsuranceMember" xlink:to="lab_kg_MaidenReinsuranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_UnderwritingIncomeLossNet_019e18df-7903-7153-af97-47dd7ee9cc87_totalLabel_en-US" xlink:label="lab_kg_UnderwritingIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Underwriting (loss) income and fee (loss) income</link:label>
    <link:label id="lab_kg_UnderwritingIncomeLossNet_label_en-US" xlink:label="lab_kg_UnderwritingIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underwriting Income Loss Net</link:label>
    <link:label id="lab_kg_UnderwritingIncomeLossNet_documentation_en-US" xlink:label="lab_kg_UnderwritingIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net premiums earned less: net losses and loss expenses, acquisition costs and general and administrative expenses directly related to underwriting activities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_UnderwritingIncomeLossNet" xlink:href="kg-20260630.xsd#kg_UnderwritingIncomeLossNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_UnderwritingIncomeLossNet" xlink:to="lab_kg_UnderwritingIncomeLossNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e18df-7a57-7c0c-9d0d-dbd6c13c5b69_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_019e18df-7903-7915-a7e8-02cceee8144b_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net incurred losses related to Prior years</link:label>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year Claims and Claims Adjustment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:to="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries_019fafd1-f742-7579-8409-76aca6c8f01a_negatedTerseLabel_en-US" xlink:label="lab_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Decrease in allowance for expected credit losses on reinsurance recoverable where credit losses were previously recognized</link:label>
    <link:label id="lab_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries_label_en-US" xlink:label="lab_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss, Recoveries</link:label>
    <link:label id="lab_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries_documentation_en-US" xlink:label="lab_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss, Recoveries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries" xlink:href="kg-20260630.xsd#kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries" xlink:to="lab_kg_ReinsuranceRecoverableAllowanceForCreditLossRecoveries" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_019e18df-7a57-7e0e-9285-9db5b2b6e5ec_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income (Loss)</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019e18df-7902-7398-b944-219dd26aa299_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnInvestments_019e18df-79c7-72dd-8e5c-8c3432bf46ce_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized investment (losses) gains</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_019e18df-79c7-729a-89f1-aca3f5447e8e_negatedLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized investment (losses) gains</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_019e18df-79c7-7b96-9ab3-0187a3fc9367_totalLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized investment (losses) gains</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnInvestments" xlink:to="lab_us-gaap_GainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_019e18df-7a57-7620-9894-a7753792fd50_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Minimum Excess Funding Requirement</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Minimum Excess Funding Requirement [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Minimum Excess Funding Requirement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:href="kg-20260630.xsd#kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:to="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_019e18df-79c6-71d7-8ff1-6eb0c09d2822_negatedLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">12 Months or More</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_019e18df-79c6-7f06-adc9-acdf9f378f62_periodStartLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Less: reinsurance recoverable on unpaid losses, January 1</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_019e18df-79c6-7b4a-9345-5eb7f6486373_periodEndLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses, June 30</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Including Reinsurance Premium Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverables" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverables" xlink:to="lab_us-gaap_ReinsuranceRecoverables" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019e18df-7a58-759d-b26f-47c57c6e2974_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_019e18df-79c7-77a9-bbe9-55e15e1a7d40_terseLabel_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative arrangement, reserves expected to be commuted, exit cost</link:label>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_label_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Reserves Expected to be Commuted, Exit Cost</link:label>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_documentation_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Reserves Expected to be Commuted, Exit Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:href="kg-20260630.xsd#kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:to="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_019e18df-7a57-7818-878b-e313ebf3f5b7_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Volatility</link:label>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Price Volatility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputPriceVolatilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:to="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_019e18df-79c6-7487-8e7b-02ebe8af7a3a_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 12 Months</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Less than Twelve Months, Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Less than Twelve Months, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesAxis_019e18df-7a57-74cd-a6e3-8b21ffa1d4e4_terseLabel_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Axis]</link:label>
    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesAxis_label_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Axis]</link:label>
    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesAxis_documentation_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:href="kg-20260630.xsd#kg_EntitiesOwnedByRelatedPartiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:to="lab_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019e18df-79c6-7bdf-ac92-e5076e8fffb9_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessAcquisitionOptionTerm_019e18df-7a57-70a8-a85a-26eaed137629_terseLabel_en-US" xlink:label="lab_kg_BusinessAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquire option term</link:label>
    <link:label id="lab_kg_BusinessAcquisitionOptionTerm_label_en-US" xlink:label="lab_kg_BusinessAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Option Term</link:label>
    <link:label id="lab_kg_BusinessAcquisitionOptionTerm_documentation_en-US" xlink:label="lab_kg_BusinessAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Acquisition, Option Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessAcquisitionOptionTerm" xlink:href="kg-20260630.xsd#kg_BusinessAcquisitionOptionTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessAcquisitionOptionTerm" xlink:to="lab_kg_BusinessAcquisitionOptionTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustLegacySegmentMember_019e18df-7a58-7811-8fc3-9da5d43fa151_verboseLabel_en-US" xlink:label="lab_kg_AmTrustLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Legacy Reinsurance</link:label>
    <link:label id="lab_kg_AmTrustLegacySegmentMember_label_en-US" xlink:label="lab_kg_AmTrustLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Legacy Segment [Member]</link:label>
    <link:label id="lab_kg_AmTrustLegacySegmentMember_documentation_en-US" xlink:label="lab_kg_AmTrustLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Legacy Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustLegacySegmentMember" xlink:href="kg-20260630.xsd#kg_AmTrustLegacySegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustLegacySegmentMember" xlink:to="lab_kg_AmTrustLegacySegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_019e18df-7903-7a2a-8dc5-1bf3a475524c_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums and losses related to policies, percentage</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Future Premiums and Losses Related to Policies</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Future Premiums and Losses Related to Policies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:to="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_019e18df-7a57-7976-98c7-d08de25ae02b_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent basis currency equivalent of maximum limit of liability attaching</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Basis Currency Equivalent of Maximum Limit of Liability Attaching</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Basis Currency Equivalent of Maximum Limit of Liability Attaching</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:to="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_019e18df-7a58-7fd5-85e9-f58da87c6f14_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_019e18df-79c7-774d-81f8-9f93a8ab482c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Investments_019e18df-79c6-7f11-a066-b69967e436c4_totalLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total investments</link:label>
    <link:label id="lab_us-gaap_Investments_label_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Investments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Investments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Investments" xlink:to="lab_us-gaap_Investments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax_019e18df-7a57-709f-9875-58c4660cab69_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized holdings (losses) gains on AFS fixed maturities</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_019e18df-79c7-773d-9d3d-50375ce3a509_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ControllingInterestOwnershipPercentage_019e18df-7a57-7726-888a-18ed0df01f9f_terseLabel_en-US" xlink:label="lab_kg_ControllingInterestOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Controlling interest, ownership percentage</link:label>
    <link:label id="lab_kg_ControllingInterestOwnershipPercentage_label_en-US" xlink:label="lab_kg_ControllingInterestOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Controlling Interest, Ownership Percentage</link:label>
    <link:label id="lab_kg_ControllingInterestOwnershipPercentage_documentation_en-US" xlink:label="lab_kg_ControllingInterestOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Controlling Interest, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ControllingInterestOwnershipPercentage" xlink:href="kg-20260630.xsd#kg_ControllingInterestOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ControllingInterestOwnershipPercentage" xlink:to="lab_kg_ControllingInterestOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_019e18df-7903-79d8-860d-7bb019f29cf6_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intercompany settlement</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_label_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Intercompany Settlement</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Intercompany Settlement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:href="kg-20260630.xsd#kg_BusinessCombinationConsiderationTransferredIntercompanySettlement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:to="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustNorthAmericaIncMember_019e18df-79c7-7c69-b3c7-a21caa493f04_terseLabel_en-US" xlink:label="lab_kg_AmTrustNorthAmericaIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust North America Inc</link:label>
    <link:label id="lab_kg_AmTrustNorthAmericaIncMember_label_en-US" xlink:label="lab_kg_AmTrustNorthAmericaIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust North America Inc [Member]</link:label>
    <link:label id="lab_kg_AmTrustNorthAmericaIncMember_documentation_en-US" xlink:label="lab_kg_AmTrustNorthAmericaIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust North America Inc</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustNorthAmericaIncMember" xlink:href="kg-20260630.xsd#kg_AmTrustNorthAmericaIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustNorthAmericaIncMember" xlink:to="lab_kg_AmTrustNorthAmericaIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member_019e18df-79c7-7569-8156-90fbbc03876c_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investments - preferred shares 4</link:label>
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    <link:label id="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Accrued Interest on Collateral Held by Related Party</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_019e18df-7903-7f55-ae3d-efc28ee5a824_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
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    <link:label id="lab_dei_EntityCurrentReportingStatus_019e18df-7903-718f-aa79-d50f4309eff3_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e18df-7902-7a2e-a359-af73f800449d_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in financing activities</link:label>
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    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
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    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss_019e18df-7903-7673-8106-64d5bfea3328_negatedLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less than 12 Months</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
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    <link:label id="lab_kg_LeahKarfunkelMember_019e18df-7903-72a7-84cc-c1d29b818e88_terseLabel_en-US" xlink:label="lab_kg_LeahKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leah Karfunkel</link:label>
    <link:label id="lab_kg_LeahKarfunkelMember_label_en-US" xlink:label="lab_kg_LeahKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leah Karfunkel [Member]</link:label>
    <link:label id="lab_kg_LeahKarfunkelMember_documentation_en-US" xlink:label="lab_kg_LeahKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leah Karfunkel</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_019e18df-7a57-70c1-9584-a7455a406903_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Purchase Price</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019e18df-7a57-7715-8570-0d0424475704_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
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    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums_019e18df-7903-74c9-93c3-b88dc65c0777_negatedLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unearned premiums</link:label>
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    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019e18df-7a57-752a-95b1-0030af6c3f19_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_019e18df-7903-7b4c-af48-32d6820f059b_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common shares from vesting of stock based compensation</link:label>
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    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
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    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_019e18df-7902-7a1b-982c-1f721d141801_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019e18df-79c7-7a02-8d9c-503cdffce098_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Data</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount_019e18df-7903-7f90-967b-a10319c8f0ff_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage ceded</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Of Ceded Business Amount</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Of Ceded Business Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:href="kg-20260630.xsd#kg_RelatedPartyTransactionPercentOfCededBusinessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:to="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedBalanceShares_019e18df-79c7-7630-9e94-077307f91978_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock owned by shareholder (in shares)</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedBalanceShares_label_en-US" xlink:label="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Balance, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedBalanceShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentOwnedBalanceShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentOwnedBalanceShares" xlink:to="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration_019e18df-79c7-7ce4-9259-277b58e98ca7_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards, with no expiry date, amount</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NotesReceivableRelatedPartyMember_019e18df-7902-7ae5-acf6-3dec3880bdc4_terseLabel_en-US" xlink:label="lab_kg_NotesReceivableRelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income from net loan receivable from AmTrust</link:label>
    <link:label id="lab_kg_NotesReceivableRelatedPartyMember_label_en-US" xlink:label="lab_kg_NotesReceivableRelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivable, Related Party [Member]</link:label>
    <link:label id="lab_kg_NotesReceivableRelatedPartyMember_documentation_en-US" xlink:label="lab_kg_NotesReceivableRelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Receivable, Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NotesReceivableRelatedPartyMember" xlink:href="kg-20260630.xsd#kg_NotesReceivableRelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NotesReceivableRelatedPartyMember" xlink:to="lab_kg_NotesReceivableRelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019e18df-79c7-766d-87d4-7e5aafa6b693_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_019e18df-79c7-7ebe-b4ae-474eb799e582_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Contractual Maturities of Fixed Maturities</link:label>
    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments Classified by Contractual Maturity Date [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:to="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MarketableSecuritiesRealizedLoss_019e18df-7903-73b4-ac0b-734f93778f01_negatedLabel_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other investments, gross losses</link:label>
    <link:label id="lab_kg_MarketableSecuritiesRealizedLoss_label_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Realized Loss</link:label>
    <link:label id="lab_kg_MarketableSecuritiesRealizedLoss_documentation_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketable Securities, Realized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MarketableSecuritiesRealizedLoss" xlink:href="kg-20260630.xsd#kg_MarketableSecuritiesRealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MarketableSecuritiesRealizedLoss" xlink:to="lab_kg_MarketableSecuritiesRealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateBondSecuritiesMember_019e18df-7903-7b35-9736-8974b6f14d05_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate bonds</link:label>
    <link:label id="lab_us-gaap_CorporateBondSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CorporateBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Bond Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateBondSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CorporateBondSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateBondSecuritiesMember" xlink:to="lab_us-gaap_CorporateBondSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense_019e18df-7903-7e96-bf6a-e15019afa06f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule for Reserve for Loss and LAE and Schedule of Prior Period Development Experienced</link:label>
    <link:label id="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Liability for Unpaid Claims and Claims Adjustment Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense" xlink:to="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProFormaMember_019e18df-79c6-7783-886c-de55fcc39274_terseLabel_en-US" xlink:label="lab_srt_ProFormaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pro Forma</link:label>
    <link:label id="lab_srt_ProFormaMember_label_en-US" xlink:label="lab_srt_ProFormaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pro Forma [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProFormaMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProFormaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProFormaMember" xlink:to="lab_srt_ProFormaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue_019e18df-79c7-7354-b87e-3c745d882551_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net present value of total distributions</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue_label_en-US" xlink:label="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Distributions, Net Present Value</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Distributions, Net Present Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:href="kg-20260630.xsd#kg_EquityMethodInvestmentsDistributionsNetPresentValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:to="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue_019e18df-7a58-7cbf-b1a6-35c5e7c13e38_totalLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:href="kg-20260630.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019e18df-7a58-76b9-bae4-837494e38a3e_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury shares, at cost (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019e18df-7a58-716b-acad-89a85c622fc7_netLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Treasury shares (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019e18df-7903-7607-9a67-8afad8e57426_totalLabel_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net premiums earned</link:label>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019e18df-7903-7738-8d52-7877b4a33920_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net premiums earned</link:label>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019e18df-7903-7a67-b1e1-7b1b3454332b_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net premiums earned</link:label>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_label_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Earned, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsEarnedNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PremiumsEarnedNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsEarnedNet" xlink:to="lab_us-gaap_PremiumsEarnedNet" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_019e18df-7903-7f29-915d-5c8bc1a86eb3_terseLabel_en-US" xlink:label="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust European Hospital Liability Quota Share Agreement</link:label>
    <link:label id="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_label_en-US" xlink:label="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust European Hospital Liability Quota Share Agreement [Member]</link:label>
    <link:label id="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_documentation_en-US" xlink:label="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust European Hospital Liability Quota Share Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:href="kg-20260630.xsd#kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:to="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeDomain_019e18df-79c7-7397-9c4b-e35d88471860_terseLabel_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Domain]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeDomain_label_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Domain]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeDomain_documentation_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:href="kg-20260630.xsd#kg_RestrictedCashAndInvestmentsTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:to="lab_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_019e18df-79c7-7a2c-b174-bd9cbbcc4c0c_terseLabel_en-US" xlink:label="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">As a percentage of total assets</link:label>
    <link:label id="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_label_en-US" xlink:label="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percent of Assets Measured at Fair Value to Total Assets</link:label>
    <link:label id="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_documentation_en-US" xlink:label="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percent of Assets Measured at Fair Value to Total Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:href="kg-20260630.xsd#kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:to="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock_019e18df-79c7-78e9-93a5-7c99eb91cce3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Intangible Assets Acquired</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Acquired [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet_019e18df-7903-7fd2-b094-f57dbb141234_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in unearned premiums</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">(Increase) Decrease in Unearned Premiums, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInUnearnedPremiumsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet" xlink:to="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019e18df-79c7-7019-a402-7a6f3884d456_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GrossPremiumsWrittenMember_019e18df-79c7-719e-bf9d-6c5c76673315_terseLabel_en-US" xlink:label="lab_kg_GrossPremiumsWrittenMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Premiums Written</link:label>
    <link:label id="lab_kg_GrossPremiumsWrittenMember_label_en-US" xlink:label="lab_kg_GrossPremiumsWrittenMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Premiums Written [Member]</link:label>
    <link:label id="lab_kg_GrossPremiumsWrittenMember_documentation_en-US" xlink:label="lab_kg_GrossPremiumsWrittenMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gross Premiums Written [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GrossPremiumsWrittenMember" xlink:href="kg-20260630.xsd#kg_GrossPremiumsWrittenMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GrossPremiumsWrittenMember" xlink:to="lab_kg_GrossPremiumsWrittenMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_019e18e3-5840-73ae-ae14-d63bdbf0b268_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019e18df-79c7-7391-b318-8d1870424c32_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReconciliationtoNetIncomeLossAbstract_019e18df-79c7-757f-a866-3201c698492f_terseLabel_en-US" xlink:label="lab_kg_ReconciliationtoNetIncomeLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation to net loss</link:label>
    <link:label id="lab_kg_ReconciliationtoNetIncomeLossAbstract_label_en-US" xlink:label="lab_kg_ReconciliationtoNetIncomeLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciliation to Net Income (Loss) [Abstract]</link:label>
    <link:label id="lab_kg_ReconciliationtoNetIncomeLossAbstract_documentation_en-US" xlink:label="lab_kg_ReconciliationtoNetIncomeLossAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reconciliation to Net Income (Loss) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReconciliationtoNetIncomeLossAbstract" xlink:href="kg-20260630.xsd#kg_ReconciliationtoNetIncomeLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract" xlink:to="lab_kg_ReconciliationtoNetIncomeLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_019e18df-7903-76c3-b9dc-79b3e3fa760e_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NumberOfNonIndependentDirectors_019e18df-79c7-73e1-9c5b-fead6be0870d_terseLabel_en-US" xlink:label="lab_kg_NumberOfNonIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of non-independent director</link:label>
    <link:label id="lab_kg_NumberOfNonIndependentDirectors_label_en-US" xlink:label="lab_kg_NumberOfNonIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Non-Independent Directors</link:label>
    <link:label id="lab_kg_NumberOfNonIndependentDirectors_documentation_en-US" xlink:label="lab_kg_NumberOfNonIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Non-Independent Directors</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfNonIndependentDirectors" xlink:href="kg-20260630.xsd#kg_NumberOfNonIndependentDirectors"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NumberOfNonIndependentDirectors" xlink:to="lab_kg_NumberOfNonIndependentDirectors" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AssetManagementAgreementMember_019e18df-7903-725c-8e56-e59810b5adaa_terseLabel_en-US" xlink:label="lab_kg_AssetManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Management Agreement</link:label>
    <link:label id="lab_kg_AssetManagementAgreementMember_label_en-US" xlink:label="lab_kg_AssetManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management Agreement [Member]</link:label>
    <link:label id="lab_kg_AssetManagementAgreementMember_documentation_en-US" xlink:label="lab_kg_AssetManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Management Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetManagementAgreementMember" xlink:href="kg-20260630.xsd#kg_AssetManagementAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AssetManagementAgreementMember" xlink:to="lab_kg_AssetManagementAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019e18df-79c6-7164-b7c9-8d64abf1c136_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019e18df-7903-793a-b5b7-222a589308d4_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive (loss) income</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnearnedPremiums_019e18df-7902-75bc-8a48-804b50e76c2f_verboseLabel_en-US" xlink:label="lab_us-gaap_UnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unearned premiums (includes $14,835 and $17,227 from related parties in 2026 and 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_UnearnedPremiums_019e18df-7902-7201-acb6-a0fb602bf9cf_terseLabel_en-US" xlink:label="lab_us-gaap_UnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unearned premiums</link:label>
    <link:label id="lab_us-gaap_UnearnedPremiums_label_en-US" xlink:label="lab_us-gaap_UnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unearned Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnearnedPremiums" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnearnedPremiums"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnearnedPremiums" xlink:to="lab_us-gaap_UnearnedPremiums" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedInvestmentNetOfLiabilities_019e18df-79c7-720d-a887-99de2952ea4f_totalLabel_en-US" xlink:label="lab_kg_RestrictedInvestmentNetOfLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total restricted investments</link:label>
    <link:label id="lab_kg_RestrictedInvestmentNetOfLiabilities_label_en-US" xlink:label="lab_kg_RestrictedInvestmentNetOfLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Investment, Net of Liabilities</link:label>
    <link:label id="lab_kg_RestrictedInvestmentNetOfLiabilities_documentation_en-US" xlink:label="lab_kg_RestrictedInvestmentNetOfLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Investment, Net of Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedInvestmentNetOfLiabilities" xlink:href="kg-20260630.xsd#kg_RestrictedInvestmentNetOfLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RestrictedInvestmentNetOfLiabilities" xlink:to="lab_kg_RestrictedInvestmentNetOfLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_019e18df-7903-7475-b74a-ff7c99ea343d_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Amortization Period</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Acquired, Weighted-Average Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member_019e18df-7a57-72d7-b80d-e7880e665a39_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investment - preferred shares 3 and 4</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 3 and 4 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 3 and 4</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:href="kg-20260630.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FoundingShareholdersMember_019e18df-79c7-7709-a23e-0c61d4c641a1_terseLabel_en-US" xlink:label="lab_kg_FoundingShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Founding shareholders</link:label>
    <link:label id="lab_kg_FoundingShareholdersMember_label_en-US" xlink:label="lab_kg_FoundingShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Founding Shareholders [Member]</link:label>
    <link:label id="lab_kg_FoundingShareholdersMember_documentation_en-US" xlink:label="lab_kg_FoundingShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Founding Shareholders [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FoundingShareholdersMember" xlink:href="kg-20260630.xsd#kg_FoundingShareholdersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FoundingShareholdersMember" xlink:to="lab_kg_FoundingShareholdersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019e18df-7903-7e9e-9fd7-d22de90f0194_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_019e18df-7a57-78c0-b4f8-9699e55d2f3a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RealEstateInvestmentsAtEquityMethodMember_019e18df-79c7-702d-9250-809973b938cb_terseLabel_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate investments at equity method</link:label>
    <link:label id="lab_kg_RealEstateInvestmentsAtEquityMethodMember_label_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investments At Equity Method [Member]</link:label>
    <link:label id="lab_kg_RealEstateInvestmentsAtEquityMethodMember_documentation_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Investments At Equity Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:href="kg-20260630.xsd#kg_RealEstateInvestmentsAtEquityMethodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:to="lab_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CashAndCashEquivalentsAndOtherMember_019e18df-79c7-719b-b4a8-db45a165d9ae_terseLabel_en-US" xlink:label="lab_kg_CashAndCashEquivalentsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_kg_CashAndCashEquivalentsAndOtherMember_label_en-US" xlink:label="lab_kg_CashAndCashEquivalentsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash And Cash Equivalents And Other [Member]</link:label>
    <link:label id="lab_kg_CashAndCashEquivalentsAndOtherMember_documentation_en-US" xlink:label="lab_kg_CashAndCashEquivalentsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash And Cash Equivalents And Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CashAndCashEquivalentsAndOtherMember" xlink:href="kg-20260630.xsd#kg_CashAndCashEquivalentsAndOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CashAndCashEquivalentsAndOtherMember" xlink:to="lab_kg_CashAndCashEquivalentsAndOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019e18df-79c7-7fa6-84e7-d45aaf066139_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_019e18df-79c7-7607-a483-0a86c0743d4f_terseLabel_en-US" xlink:label="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income and net realized and unrealized investment (losses) gains</link:label>
    <link:label id="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_label_en-US" xlink:label="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income and Gain (Loss) on Investments, Net</link:label>
    <link:label id="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_documentation_en-US" xlink:label="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Income and Gain (Loss) on Investments, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:href="kg-20260630.xsd#kg_InvestmentIncomeAndGainLossOnInvestmentsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:to="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_019e18df-79c7-7f92-a314-3ac59ddd5c64_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_019e18df-7a57-7cf3-bfd0-52ba999c09fd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:to="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019e18df-79c7-7539-828a-20236eefbdc2_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member_019e18df-7903-753c-ab53-62473d4a7562_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investment - preferred shares 1 and 2</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 1 and 2 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 1 and 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:href="kg-20260630.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract_019e18df-79c7-74dc-8e18-9614ed7c6c38_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in assets &#8211; (increase) decrease:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_019e18df-7903-7335-be27-11ae8117fa71_terseLabel_en-US" xlink:label="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">European Hospital Liability Quota Share</link:label>
    <link:label id="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_label_en-US" xlink:label="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">European Hospital Liability Quota Share Agreement [Member]</link:label>
    <link:label id="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_documentation_en-US" xlink:label="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">European Hospital Liability Quota Share Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:href="kg-20260630.xsd#kg_EuropeanHospitalLiabilityQuotaShareAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:to="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019e18df-79c7-7905-8f70-b6c2a608a214_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019e18df-7903-7277-beb5-11881465f3c5_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_019e18df-79c7-7ec4-ad80-7a07a9f25a4d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Securities [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Securities [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:to="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ExternalCreditRatingStandardPoorsMember_019e18df-79c6-7f89-afaf-8725a3ddd01e_terseLabel_en-US" xlink:label="lab_srt_ExternalCreditRatingStandardPoorsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">External Credit Rating, Standard &amp; Poor's [Domain]</link:label>
    <link:label id="lab_srt_ExternalCreditRatingStandardPoorsMember_label_en-US" xlink:label="lab_srt_ExternalCreditRatingStandardPoorsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">External Credit Rating, Standard &amp; Poor's [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ExternalCreditRatingStandardPoorsMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ExternalCreditRatingStandardPoorsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ExternalCreditRatingStandardPoorsMember" xlink:to="lab_srt_ExternalCreditRatingStandardPoorsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_019e18df-79c7-77a8-a366-329fbb40398f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Treatment for the Combination</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsPolicy" xlink:to="lab_us-gaap_BusinessCombinationsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_019e18df-79c6-7ce1-aeba-6fef000abb6f_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceTextBlock_019e18df-7903-7408-9165-de63dc6f1b23_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance</link:label>
    <link:label id="lab_us-gaap_ReinsuranceTextBlock_label_en-US" xlink:label="lab_us-gaap_ReinsuranceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceTextBlock" xlink:to="lab_us-gaap_ReinsuranceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_019e18df-79c7-74f1-a73e-5362503a8db5_terseLabel_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funds withheld receivable: (Allowance for expected credit losses: 2026: $2; 2025: $2)</link:label>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_019e18df-79c7-7f68-add9-9ab9166abb06_verboseLabel_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Funds withheld receivable</link:label>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_label_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Funds Held under Reinsurance Agreements, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FundsHeldUnderReinsuranceAgreementsAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:to="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_019e18df-7903-7062-983a-3f99112e8daa_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense_019e18df-7903-753d-98ab-13a546cb3b4e_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net paid losses</link:label>
    <link:label id="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Claims Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForLossesAndLossAdjustmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:to="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquityMethodInvestmentsInvesteeRevenue_019e18df-7a57-715a-ae25-90ed332b2718_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investee Revenue</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsInvesteeRevenue_label_en-US" xlink:label="lab_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments Investee Revenue</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsInvesteeRevenue_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments Investee Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:href="kg-20260630.xsd#kg_EquityMethodInvestmentsInvesteeRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:to="lab_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019e18df-7903-72a5-a422-093c7b859984_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities (includes $25,163 and $16,443 from related parties in 2026 and 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019e18df-7903-7f3d-8668-6ec634139328_verboseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities and Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:to="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_019e18df-7903-7ddb-ac13-d982f6a92172_terseLabel_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash acquired from purchase of business</link:label>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_label_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Acquired from Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAcquiredFromAcquisition" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAcquiredFromAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAcquiredFromAcquisition" xlink:to="lab_us-gaap_CashAcquiredFromAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StandardPoorsAAARatingMember_019e18df-7902-7d04-abe9-f8fe393a3ec6_terseLabel_en-US" xlink:label="lab_srt_StandardPoorsAAARatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AAA</link:label>
    <link:label id="lab_srt_StandardPoorsAAARatingMember_label_en-US" xlink:label="lab_srt_StandardPoorsAAARatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, AAA Rating [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StandardPoorsAAARatingMember" xlink:to="lab_srt_StandardPoorsAAARatingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019e18df-7a57-7663-bfaa-8d5fb1353546_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross_019e18df-7a57-77d5-80f7-122ebf1929e7_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross loss and LAE</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Direct</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:to="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross_019e18df-7a57-78f3-beb6-29240bffbfaf_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverables on paid losses, gross</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables on Paid Losses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverablesOnPaidLossesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:to="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019e18df-7903-7384-9083-19412f407353_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_DebtInstrumentAxis_019e18df-7a57-71de-9276-528c5e9e608b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities_019e18df-79c6-7a01-b20f-a41d5cf6cefc_negatedLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Accrued Expenses and Other Liabilities</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Accrued Expenses and Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet_019e18df-7902-76ae-a667-6a7779f87a12_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Reinsurance Balances Receivable, Net</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Reinsurance Balances Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet" xlink:href="kg-20260630.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensation_019e18df-79c7-7ce1-ab0d-806c61afc9ae_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
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    <link:label id="lab_kg_MeasurementInputDiscountForLackOfMarketabilityOPMMember_019e18df-7902-704d-b738-e0ef06c055ce_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputDiscountForLackOfMarketabilityOPMMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount for Lack of Marketability - OPM</link:label>
    <link:label id="lab_kg_MeasurementInputDiscountForLackOfMarketabilityOPMMember_label_en-US" xlink:label="lab_kg_MeasurementInputDiscountForLackOfMarketabilityOPMMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement&#8203; Input &#8203;Discount &#8203;For &#8203;Lack &#8203;Of &#8203;Marketability, OPM [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputDiscountForLackOfMarketabilityOPMMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputDiscountForLackOfMarketabilityOPMMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement&#8203; Input &#8203;Discount &#8203;For &#8203;Lack &#8203;Of &#8203;Marketability, OPM</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputDiscountForLackOfMarketabilityOPMMember" xlink:href="kg-20260630.xsd#kg_MeasurementInputDiscountForLackOfMarketabilityOPMMember"/>
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    <link:label id="lab_kg_PremiumWrittenGrossAndNet_019e18df-79c7-7770-80a7-5fddefcba069_verboseLabel_en-US" xlink:label="lab_kg_PremiumWrittenGrossAndNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross and net premiums written</link:label>
    <link:label id="lab_kg_PremiumWrittenGrossAndNet_label_en-US" xlink:label="lab_kg_PremiumWrittenGrossAndNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Written Gross And Net</link:label>
    <link:label id="lab_kg_PremiumWrittenGrossAndNet_documentation_en-US" xlink:label="lab_kg_PremiumWrittenGrossAndNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premium Written Gross And Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumWrittenGrossAndNet" xlink:href="kg-20260630.xsd#kg_PremiumWrittenGrossAndNet"/>
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    <link:label id="lab_kg_SecuritiesContinuousUnrealizedLossPositionFairValueTableTextBlock_019e18df-79c6-7671-b304-af0e526149c0_terseLabel_en-US" xlink:label="lab_kg_SecuritiesContinuousUnrealizedLossPositionFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fixed Maturities in an Unrealized Loss Position and Aggregate Fair Value</link:label>
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    <link:label id="lab_us-gaap_ForeignGovernmentDebtMember_019e18df-7a57-7a65-bd46-390a133ba2c1_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignGovernmentDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-U.S. government bonds</link:label>
    <link:label id="lab_us-gaap_ForeignGovernmentDebtMember_019e18df-7a57-76b5-bfef-dac0140fe3a0_verboseLabel_en-US" xlink:label="lab_us-gaap_ForeignGovernmentDebtMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-U.S. government bonds</link:label>
    <link:label id="lab_us-gaap_ForeignGovernmentDebtMember_label_en-US" xlink:label="lab_us-gaap_ForeignGovernmentDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Government Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignGovernmentDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignGovernmentDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignGovernmentDebtMember" xlink:to="lab_us-gaap_ForeignGovernmentDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_019e18df-7903-78eb-93ed-5a6c34c5f894_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction amount (returned)</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Amounts of Transaction</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareBasic_019e18df-79c7-7117-98b2-c7e7c5eeee64_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (loss) earnings per share attributable to Kestrel shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
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    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_019e18df-7903-7ced-8c5b-8e800b4d65f1_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
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    <link:label id="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock_019e18df-79c6-732f-8dfe-b0a16850ff4f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Class of Treasury Stock</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Treasury Stock [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseReportedClaimsAmount_019e18df-7902-70e6-9344-8dbfcac289c2_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseReportedClaimsAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for reported loss and LAE</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseReportedClaimsAmount_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseReportedClaimsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Reported Claims, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseReportedClaimsAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseReportedClaimsAmount"/>
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    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019e18df-7902-77f8-8929-e5bfdbc141fc_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commission and other acquisition expenses</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019e18df-7902-7a08-8943-b37fb84d444d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Commission and other acquisition expenses</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019e18df-7902-7c51-b1fe-1477de20507e_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Commission and other acquisition expenses</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
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    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_019e18df-79c6-7ec0-b45f-12708e23d907_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
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    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiability_019e18df-79c7-75c5-8661-f7efa0f559ff_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent consideration</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiability_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationContingentConsiderationLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock_019e18df-79c7-752d-934a-27d8f798b022_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure and Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock"/>
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    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
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    <link:label id="lab_us-gaap_InsuranceAbstract_019e18df-7903-7d86-9fbd-709319579cc9_terseLabel_en-US" xlink:label="lab_us-gaap_InsuranceAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance [Abstract]</link:label>
    <link:label id="lab_us-gaap_InsuranceAbstract_label_en-US" xlink:label="lab_us-gaap_InsuranceAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InsuranceAbstract"/>
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    <link:label id="lab_us-gaap_InvestmentTypeExtensibleEnumeration_019e18df-79c7-7a2d-a224-932bb32b0019_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Type [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Type [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentTypeExtensibleEnumeration"/>
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    <link:label id="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage_label_en-US" xlink:label="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Assets And Liabilities, Retroceded, Percentage</link:label>
    <link:label id="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage_documentation_en-US" xlink:label="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance, Assets And Liabilities, Retroceded, Percentage</link:label>
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    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
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    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyTable_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Retention [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionPolicyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRetentionPolicyTable"/>
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    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward"/>
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    <link:label id="lab_us-gaap_AssumedPremiumsEarned_019e18df-7a57-7f8e-b934-54bd74705daa_terseLabel_en-US" xlink:label="lab_us-gaap_AssumedPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed</link:label>
    <link:label id="lab_us-gaap_AssumedPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_AssumedPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assumed Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssumedPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssumedPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssumedPremiumsEarned" xlink:to="lab_us-gaap_AssumedPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable_019e18df-7a58-7365-ab2e-fdd0174e7bbd_terseLabel_en-US" xlink:label="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Cash and Investments [Table]</link:label>
    <link:label id="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable_label_en-US" xlink:label="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Cash and Investments [Table]</link:label>
    <link:label id="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable_documentation_en-US" xlink:label="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Cash and Investments [Table]</link:label>
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    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling_019e18df-7903-7600-b2cd-4a51bf061b7d_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commission rate, adjustment criteria, loss ratio ceiling</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Adjustment Criteria, Loss Ratio Ceiling</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Adjustment Criteria, Loss Ratio Ceiling</link:label>
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    <link:label id="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_019e18df-7902-7698-ace7-a240a1d28ca5_terseLabel_en-US" xlink:label="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BBB+, BBB, BBB-</link:label>
    <link:label id="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_label_en-US" xlink:label="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, BBB Plus, BBB, BBB Minus Rating [Member]</link:label>
    <link:label id="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_documentation_en-US" xlink:label="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, BBB Plus, BBB, BBB Minus Rating [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:href="kg-20260630.xsd#kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:to="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameAxis_019e18df-7903-7694-a289-11d541d9d444_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:label id="lab_us-gaap_PlanNameAxis_label_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameAxis" xlink:to="lab_us-gaap_PlanNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_019e18df-79c7-7645-a670-25c678ae9d15_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:to="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:to="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable_019e18df-7a57-75e5-93a5-75680cb4e314_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Premiums Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPremiumsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_LossContingencyLossInPeriod_label_en-US" xlink:label="lab_us-gaap_LossContingencyLossInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual, Loss (Reversal of Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyLossInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyLossInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyLossInPeriod" xlink:to="lab_us-gaap_LossContingencyLossInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_019e18df-79c7-70b3-853e-920d5bbcec7e_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Amortization at June&#160;30, 2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, after Accumulated Amortization [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNetAbstract"/>
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    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock_019e18df-7903-72b0-8eda-3ab943c19dc7_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for Loss and Loss Adjustment Expenses</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefits and Unpaid Claims Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_LongTermDebtTextBlock_019e18df-7a57-7fc7-9900-e2fb8b78928a_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtTextBlock_label_en-US" xlink:label="lab_us-gaap_LongTermDebtTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtTextBlock" xlink:to="lab_us-gaap_LongTermDebtTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod_019e18df-7a57-71bd-b95d-998a5d3d5cd3_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investments</link:label>
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    <link:label id="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Recorded with Equity Method</link:label>
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    <link:label id="lab_us-gaap_OtherDebtSecuritiesMember_019e18df-79c6-7c14-9d99-c1127a49f03e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_us-gaap_OtherDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_OtherDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Debt Obligations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherDebtSecuritiesMember" xlink:to="lab_us-gaap_OtherDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_019e18df-79c7-76a5-8950-1e03ff9a39b1_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EQUITY</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract"/>
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    <link:label id="lab_dei_EntityAddressCountry_019e18df-7a57-75fd-b635-2bbb0a478d35_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCountry" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Country</link:label>
    <link:label id="lab_dei_EntityAddressCountry_label_en-US" xlink:label="lab_dei_EntityAddressCountry" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Country</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCountry"/>
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    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock_019e18df-7a57-7b25-b699-8e61bf4da6c9_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allowance for Expected Credit Losses on Reinsurance Recoverable</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock"/>
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    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesDiluted_019e18df-7902-7b50-a35f-a516ca4a2b97_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesDiluted" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amount allocated to participating common shareholders, diluted</link:label>
    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesDiluted_label_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Participating Securities, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesDiluted"/>
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    <link:label id="lab_kg_GainLossOnEquityMethodInvestments_label_en-US" xlink:label="lab_kg_GainLossOnEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Equity Method Investments</link:label>
    <link:label id="lab_kg_GainLossOnEquityMethodInvestments_documentation_en-US" xlink:label="lab_kg_GainLossOnEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Equity Method Investments</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationAsset_019e18df-7903-7d86-b1b1-0e71a3817eb9_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Receivable</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationAsset_019e18df-7903-796e-871a-4c6ced68e596_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Contingent receivable</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationAsset_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Asset</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ShareRepurchaseProgramAxis_019e18df-7a58-7ff6-91c9-2eafe011a5ed_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
    <link:label id="lab_srt_ShareRepurchaseProgramAxis_label_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ShareRepurchaseProgramAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ShareRepurchaseProgramAxis"/>
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    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_019e18df-7a57-784b-a046-df9efa2d0ff5_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
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    <link:label id="lab_kg_ScheduleofFixedMaturitiesTable_019e18df-7902-7036-9d18-22bee175f65b_terseLabel_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fixed Maturities Table [Table]</link:label>
    <link:label id="lab_kg_ScheduleofFixedMaturitiesTable_label_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fixed Maturities [Table]</link:label>
    <link:label id="lab_kg_ScheduleofFixedMaturitiesTable_documentation_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Fixed Maturities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleofFixedMaturitiesTable" xlink:href="kg-20260630.xsd#kg_ScheduleofFixedMaturitiesTable"/>
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    <link:label id="lab_us-gaap_OtherCommitment_019e18df-7a57-7784-85dc-b3dd8d6c7f0a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantees provided to lenders on behalf of real estate joint venture</link:label>
    <link:label id="lab_us-gaap_OtherCommitment_label_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitment" xlink:to="lab_us-gaap_OtherCommitment" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_019e18df-7903-75a0-b10f-69286ee5e6ae_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Privately held preferred stocks</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:href="kg-20260630.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_019e18df-7a57-7eaf-9f6a-ae02b2115e2f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:to="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNetAbstract_019e18df-7903-7b79-9aca-12f4703006e5_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNetAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNetAbstract"/>
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    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
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    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019e18df-7902-78f3-9f81-6ddcdbdcb394_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total consideration effectively transferred</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
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    <link:label id="lab_kg_OtherPrivatelyHeldInvestmentsMember_019e18df-7a57-7d7e-b9e8-2de7d29bb3cd_terseLabel_en-US" xlink:label="lab_kg_OtherPrivatelyHeldInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Privately held equity investments</link:label>
    <link:label id="lab_kg_OtherPrivatelyHeldInvestmentsMember_label_en-US" xlink:label="lab_kg_OtherPrivatelyHeldInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Privately Held Investments [Member]</link:label>
    <link:label id="lab_kg_OtherPrivatelyHeldInvestmentsMember_documentation_en-US" xlink:label="lab_kg_OtherPrivatelyHeldInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Privately Held Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherPrivatelyHeldInvestmentsMember" xlink:href="kg-20260630.xsd#kg_OtherPrivatelyHeldInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OtherPrivatelyHeldInvestmentsMember" xlink:to="lab_kg_OtherPrivatelyHeldInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVentureMember_019e18df-79c7-7855-8b8f-6f5eb3a8a4da_terseLabel_en-US" xlink:label="lab_kg_SilverstoneVentureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Silverstone Ventures</link:label>
    <link:label id="lab_kg_SilverstoneVentureMember_label_en-US" xlink:label="lab_kg_SilverstoneVentureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Silverstone Venture [Member]</link:label>
    <link:label id="lab_kg_SilverstoneVentureMember_documentation_en-US" xlink:label="lab_kg_SilverstoneVentureMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Silverstone Venture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVentureMember" xlink:href="kg-20260630.xsd#kg_SilverstoneVentureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SilverstoneVentureMember" xlink:to="lab_kg_SilverstoneVentureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract_019e18df-79c7-75f7-b79e-7d60e3f78e33_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums earned</link:label>
    <link:label id="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract_label_en-US" xlink:label="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Earned, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:to="lab_us-gaap_ReinsurancePremiumsForInsuranceCompaniesByProductSegmentNetAmountAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnInvestmentsTextBlock_019e18df-79c7-777b-8d2d-aaa2f2ede738_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Realized and Unrealized Investment Gains (Losses)</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Securities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestmentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnInvestmentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnInvestmentsTextBlock" xlink:to="lab_us-gaap_GainLossOnInvestmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019e18df-79c7-7559-9cf8-0fa9854d6b1d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_019e18df-7903-740f-94f2-cd6445cb6c6d_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group Ltd share price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_019e18df-7903-7f40-a39f-149449db38df_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group Ltd share price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionSharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionSharePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionSharePrice" xlink:to="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019e18df-7a57-7e41-b61c-c6a5ac77d46e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underwriting-related derivative liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorNotesMember_019e18df-7903-7598-a6ad-4e0ac4c9f010_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_label_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotesMember" xlink:to="lab_us-gaap_SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019e18df-7903-7086-94a5-85602df42765_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_TerryAndLukeLedbetterMember_019e18df-79c7-7d6b-8d5b-366fe7a25f11_terseLabel_en-US" xlink:label="lab_kg_TerryAndLukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Terry and Luke Ledbetter</link:label>
    <link:label id="lab_kg_TerryAndLukeLedbetterMember_label_en-US" xlink:label="lab_kg_TerryAndLukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Terry and Luke Ledbetter [Member]</link:label>
    <link:label id="lab_kg_TerryAndLukeLedbetterMember_documentation_en-US" xlink:label="lab_kg_TerryAndLukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Terry and Luke Ledbetter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_TerryAndLukeLedbetterMember" xlink:href="kg-20260630.xsd#kg_TerryAndLukeLedbetterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_TerryAndLukeLedbetterMember" xlink:to="lab_kg_TerryAndLukeLedbetterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LoanAgreementMember_019e18df-7903-74e4-a605-8e05d594a139_terseLabel_en-US" xlink:label="lab_kg_LoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Agreement</link:label>
    <link:label id="lab_kg_LoanAgreementMember_label_en-US" xlink:label="lab_kg_LoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Agreement [Member]</link:label>
    <link:label id="lab_kg_LoanAgreementMember_documentation_en-US" xlink:label="lab_kg_LoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LoanAgreementMember" xlink:href="kg-20260630.xsd#kg_LoanAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LoanAgreementMember" xlink:to="lab_kg_LoanAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019e18df-7903-7928-8c82-ba6f23b30580_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: income tax (benefit) expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019e18df-7903-71ce-b388-0ce14e4d33b6_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Income tax (benefit) expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019e18df-7903-769b-9556-f14981a22a22_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income tax benefit</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralizedLoanObligationsMember_019e18df-79c7-7969-a805-e1930cb67d23_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_CollateralizedLoanObligationsMember_label_en-US" xlink:label="lab_us-gaap_CollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralizedLoanObligationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CollateralizedLoanObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralizedLoanObligationsMember" xlink:to="lab_us-gaap_CollateralizedLoanObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsDeferredIncome_019e18df-7a58-74de-a646-a64e197681e5_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsDeferredIncome_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Deferred Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsDeferredIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:to="lab_us-gaap_DeferredTaxAssetsDeferredIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndInvestments_019e18df-7902-74dd-adca-5c7a39a74dbf_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents and investments</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndInvestments_019e18df-7902-7b26-a39d-8ba58363f4f5_totalLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total restricted cash and investments</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndInvestments_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashAndInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndInvestments" xlink:to="lab_us-gaap_RestrictedCashAndInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsReceivableAtCarryingValue_019e18df-7a57-7e79-a4b3-96cda5cead70_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net (includes $0 and $2 from related parties in 2026 and 2025, respectively. Allowance for expected credit losses: 2026 - $14; 2025 - $14)</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAtCarryingValue_019e18df-7a57-76db-a90c-4fff4eced467_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PremiumsReceivableAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsReceivableAtCarryingValue" xlink:to="lab_us-gaap_PremiumsReceivableAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019e18df-79c7-756e-ab65-2233219512eb_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted cash flows</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019e18df-7a57-7b62-a634-41dea9f2d540_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
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