  By connecting Hund's physics with flat band physics, we establish an exact
result for studying ferromagnetism in a multiorbital system. We consider a
two-layer model consisting of a $p_x$, $p_y$-orbital honeycomb lattice layer
and an $f$-orbital triangular lattice layer with sites aligned with the centers
of the honeycomb plaquettes. The system features a flat band that admits a
percolation representation for an appropriate chemical potential difference
between the two layers. In this representation, the ground state space is
spanned by maximum-spin clusters of localized single-particle states, and
averaging over the ground states yields a correlated percolation problem with
weights due to the spin degeneracy of the clusters. A
paramagnetic-ferromagnetic transition occurs as the band approaches half
filling and the ground states become dominated by states with a large
maximum-spin cluster, as shown by Monte Carlo simulation.
