  Rotating photon gas exhibits a chirality separation along the angular
velocity which is manifested through a generation of helicity and zilch
currents. In this paper we study this system using the corresponding Wigner
function and construct elements of the covariant chiral kinetic theory for
photons from first principles. The Wigner function is solved order-by-order in
$\hbar$ and the unconstrained terms are fixed by matching with quantum field
theory results. We further consider the zilch and helicity currents and show
that both manifestations of the chirality transport originate in the Berry
phase of photons similarly to other chiral effects. Constructing the kinetic
description from the Wigner function we find that the frame vector needed to
fix the definition of spin of a massless particle is, in fact, the vector of
the residual gauge freedom for the free Maxwell theory. We also briefly comment
on the possible relation between vortical responses in rotating systems of
massless particles and the anomalies of underlying quantum field theory.
