<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-03-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001604665</issuerCik>
        <issuerName>Westlake Chemical Partners LP</issuerName>
        <issuerTradingSymbol>WLKP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001545199</rptOwnerCik>
            <rptOwnerName>Lumpkins David</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2801 POST OAK BLVD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 600</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77056</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units (Limited Partner Interests)</value>
            </securityTitle>
            <transactionDate>
                <value>2017-03-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>25.4161</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">In accordance with the Securities and Exchange Commission's No Action Letter dated June 25, 2008, we have aggregated the purchase that occurred on March 9, 2017 for ease of reporting.  The price reported in Column 4 is a weighted average price.  These common units were purchased in multiple transactions ranging from $25.25 to $25.7, inclusive.  The reporting person undertakes to provide to Westlake Chemical Partners LP, any security holder of Westlake Chemical Partners LP or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of common units purchased at each separate price within the ranges set forth in this footnote (1) to this Form 4.</footnote>
    </footnotes>

    <remarks>Mr. Lumpkins is a Director of Westlake Chemical Partners GP LLC, the general partner of Westlake Chemical Partners LP.</remarks>

    <ownerSignature>
        <signatureName>David Lumpkins by J. Iglesias POA</signatureName>
        <signatureDate>2017-03-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
