A search for a heavy W' resonance decaying to one B or T vector-like quark and a top or bottom quark, respectively, is presented. The search uses proton-proton collision data collected in 2016 with the CMS detector at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$ at $\sqrt{s} =$ 13 TeV. Both decay channels result in a final state with a top quark, a Higgs boson, and a b quark, each produced with significant energy. The all-hadronic decays of both the Higgs boson and the top quark are considered. The final-state jets, some of which correspond to merged decay products of a boosted top quark and a Higgs boson, are selected using jet substructure techniques, which help to suppress standard model backgrounds. A W' boson signal would appear as a narrow peak in the invariant mass distribution of these jets. No significant deviation in data with respect to the standard model background predictions is observed. Cross section upper limits on W' boson production in the top quark, Higgs boson, and b quark decay mode are set as a function of the W' mass, for several vector-like quark mass hypotheses. These are the first limits for W' boson production in this decay channel, and cover a range of 0.01 to 0.43 pb in the W' mass range between 1.5 and 4.0 TeV.