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The Mn atoms in the hexagonal metal Sc₃Mn₃Al₇Si₅ are arranged on a Kagome lattice. We have studied the phonon density of states (DOS) in Sc₃Mn₃Al₇Si₅ using both inelastic neutron scattering (INS) measurements and ab initio calculations. The simulation of the single phonon DOS agrees well with the results of INS measurement, matching both the peak positions and their intensities. This consistency between experimental and theoretical results suggests that phonon anharmonicity is not significant in this material, and further evidence comes from a very small multiphonon contribution to the measured DOS, and the absence of softening or broadening of the phonon DOS with increasing temperature. The partial phonon DOS calculation shows that the phonon DOS arises mainly from the Sc atoms, while that of the Mn atoms makes only a small contribution. The lattice component of the specific heat is estimated from the INS measured phonon DOS, finding that it accounts for ~82% of the measured specific heat at 200 K. After the lattice component of the specific heat, the lattice dilational specific heat, and the electronic specific heat are subtracted, a magnetic contribution to the specific heat is inferred.