A full microscopic description of the correlated insulators and superconductivity that occur in the flat bands of magic angle twisted bilayer graphene has not yet been found. Electronic transport and scanning tunnelling microscopy experiments have suggested a dichotomy between local and extended electronic orbitals, but definitive evidence for the coexistence of these two carrier types is still sought after. Here we report local photothermoelectric measurements in the flat electronic bands of symmetrically twisted trilayer graphene. We observe oscillations of the Seebeck coefficient around integer fillings of the flat band, signalling the presence of electron correlations, coupled with a breakdown of the predictions of the Mott formula. Our measurements reveal an overall negative offset of the Seebeck coefficient and peaks of the local photovoltage values at all positive integer fillings of the moiré superlattice. This further indicates a deviation from the classical two-band semiconductor Seebeck response. Our findings may be interpreted using the heavy-fermion model in the topological flat bands of moiré graphene and highlight an avenue to apply local thermoelectric measurements to other strongly correlated materials.