Flat-band (FB) systems originating from special lattice geometry like in kagome metals as well as localized orbitals in the materials such as heavy-fermion (HF) compounds have induced intensive interest due to their band topology and strong electron correlation effects, leading to emergent quantum states of matter. However, how these two distinct types of FBs coexist and interact within a single material remains largely unexplored. Here, we report that YbCr6Ge6, hosting both Cr kagome lattice and localized Yb-4f electrons, exhibits HF behaviors and an antiferromagnetic ground state with a transition temperature TN = 3 K. Angle-resolved photoemission spectroscopy (ARPES) reveals the coexistence of Cr-kagome-derived and Yb-4f-derived FBs near the Fermi energy level EF. Photon-energy-dependent ARPES measurements distinguish the bulk dispersive kagome-derived bands from the nearly momentum-independent Yb-4f states, while clear spectroscopic signatures of c-f hybridization are observed between the Yb-4f FBs and kagome-derived conduction bands. The high density of states associated with the Cr kagome FB and the c-f hybridization provide microscopic insight into the enhanced electronic correlations and magnetic ordering in YbCr6Ge6. Our findings establish YbCr6Ge6 as a promising platform for exploring the interplay between kagome FB physics and strong f-electron correlations.