A new kinetic Monte Carlo method for modeling phonon transport in quantum dot superlattices is presented. The method uses phonon scattering phase functions and cross sections to describe collisions between phonons and quantum dots. The phase functions and cross sections are generated using molecular dynamics simulation, which is capable of including atomistic effects otherwise unavailable in Monte Carlo approaches. The method is demonstrated for a test case featuring a Si-Ge quantum dot superlattice, and the model is compared against published experiments. It is found that molecular dynamics-derived cross sections must be weighted by diffuse mismatch model-type weighting factors in order to satisfy detailed balance considerations. Additionally, it is found that thin alloy “base layer” films strongly reduce thermal conductivity in these systems and must be included in the modeling to obtain agreement with published experimental data.