Keep Our Pension Promises Act This bill repeals the elimination of the pension anti-cutback provisions under the Multiemployer Pension Reform Act of 2014. The anti-cutback provisions prohibit reductions in pension benefits to participants in multiemployer pension plans. The bill amends the Employee Retirement Income Security Act of 1974 (ERISA), with respect to partitions of eligible multiemployer plans, to modify the procedures and allow plan sponsors to petition the Pension Benefit Guaranty Corporation (PBGC) for a partition of additional financially-troubled pension plans. The PBGC must establish a legacy fund to cover the administrative and benefit costs resulting from a partition. The Department of the Treasury must transfer amounts to the fund that are equal to the increase in revenues as a result of specified provisions of this bill that amend the Internal Revenue Code. The provisions amend the Internal Revenue Code to: (1) impose a limit of $1 million on the exemption of the gain from the exchange of real property in a like kind exchange, (2) prohibit the use of like kind exchanges for collectibles, and (3) limit contributions and require increased minimum distributions for individuals with certain retirement plans with balances that exceed $5 million (adjusted for inflation after 2017). The bill amends the federal bankruptcy code to assign first claim priority to pension obligations under ERISA.