It is important to determine an appropriate computational method for obtaining accurate thermochemical properties of large biodiesel molecules such as methyl linolenate. In this study, we use Kohn-Sham density functional theory (DFT) and coupled cluster theory to calculate bond dissociation enthalpies (BDEs) of seven fragment molecules of methyl linolenate, in particular, propene, methyl formate, cis-3-hexene, 1,4-pentadiene, 1-pentene, butane, and methyl butanoate. The results are compared to BDEs obtained from experiments and to Oyeyemi et al.'s multireference averaged coupled pair functional (MRACPF2) calculations. We found that with extrapolation to the complete basis set (CBS) limit, the BDEs derived from coupled cluster calculations with single, double, and triple excitations (CCSDT) and from CCSDT with a perturbative treatment of connected quadruple excitations, CCSDT(2)Q/CBS, are closer to the available experimental values than those obtained by MRACPF2 for propene and methyl formate. The CCSDT/CBS calculations were chosen as the reference for validating the DFT methods. Among the density functionals, we found that M08-HX has the best performance with a mean unsigned deviation (MUD) from CCSDT/CBS of only 1.0 kcal/mol, whereas the much more expensive MRACPF2 has an MUD of 1.1 kcal/mol. We then used the most successfully validated density functionals to calculate the BDEs of methyl linolenate and compared the results with the MRACPF2 BDEs. The present study identifies several Kohn-Sham exchange-correlation functionals that should be useful for modeling ester combustion, especially the M08-HX, M06-2X, M05-2X, M08-SO, and MPWB1K global-hybrid meta functionals, the M11 and MN12-SX range-separated-hybrid meta functionals, the B97 range-separated hybrid gradient approximation functional, and the SOGGA11-X global-hybrid gradient approximation functional.