Flat bands in kagome lattices provide a prominent route to strongly correlated electronic states. Here we report charge and thermal transport measurements on single crystals of CsCr₆Sb₆, a kagome Kondo system arising from the hybridization between flat and dispersive bands. The Seebeck coefficient and Nernst signal increase rapidly below TF∼70 K, concomitant with the emergence of short-range antiferromagnetic correlations and flat-band resonance. The Nernst coefficient in the intermediate-temperature range of ∼30-80 K further follows the universal scaling reported for prototypical heavy-fermion compounds, consistent with the development of strongly renormalized quasiparticles associated with hybridization. Both the Seebeck and Nernst responses reach extrema at a lower temperature Tp∼20-25 K, where phonon drag and correlated quasiparticles may both contribute. These results reveal a hybridization-induced enhancement of the thermoelectric response and establish CsCr₆Sb₆ as a kagome platform for probing flat-band-derived Kondo physics through thermoelectric transport.