Orbital-selective correlations in kagome flat bands of Co$_3$Sn$_2$S$_2$

Geometrical flat bands provide an ideal platform for studying electronic correlations and quantum-geometric effects. Although the ferromagnetic Weyl semimetal \CoSnS is generally considered a moderately correlated system, recent spectroscopy experiments have revealed a flat-band feature near the Fermi level ($\EF$) that is absent in conventional density functional theory (DFT) calculations. Using DFT plus dynamical mean-field theory and a minimal kagome model, we show that this feature arises not from heavy-fermion-like dynamical band renormalization, but from the shifting of a $d_{x^2-y^2}$ dominated geometrical kagome flat band toward $\EF$ driven by orbital- and spin-dependent self-energies. The relocated flat band enhances the local Berry curvature near $\EF$, resulting in a strongly energy-dependent anomalous Hall conductivity and a giant anomalous Nernst effect. Our findings establish an orbital-selective correlation mechanism for positioning geometrical flat bands at $\EF$, and propose anomalous thermoelectric transport as a sensitive probe of flat band induced topology.