Materials where flattened electronic dispersions arise from destructive phase interference, rather than localized orbitals, have emerged as promising platforms for studying emergent quantum phenomena. Crucial next steps involve tuning such flat bands to the Fermi level, where they can be studied at low energy scales, and assessing their potential for practical applications. Here, we show that the interplay of highly dispersive and ultraflat bands inherent to these systems can lead to extreme interband scattering-induced electron-hole asymmetry, which can be harnessed in thermoelectrics. Our comprehensive theoretical and experimental investigation of Ni3In1−xSnx kagome metals supports this concept, showing that it could lead to thermoelectric performance on par with state-of-the-art semiconductors such as Bi2Te3. In Ni3 In, scattering-induced electron-hole asymmetry is, however, subdued by an exotic conduction mechanism arising from quantum tunneling of charge carriers between Dirac bands, unrelated to the flat band itself.We outline strategies to selectively switch off this tunneling transport through negative chemical pressure or strain. Our study proposes a new direction to explore in topological flat-band systems and vice versa introduces a novel tuning knob for thermoelectric materials. References: PHYSICAL REVIEW X 15, 021054 (2025)