We consider a class of stochastic kinetic equations, depending on two time scale separation parameters $ε$ and $δ$: the evolution equation contains singular terms with respect to $ε$, and is driven by a fast ergodic process which evolves at the time scale $t/δ^2$. We prove that when $(ε,δ)\to (0,0)$ the density converges to the solution of a linear diffusion PDE. This is a mixture of diffusion approximation in the PDE sense (with respect to the parameter $ε$) and of averaging in the probabilistic sense (with respect to the parameter $δ$). The proof employs stopping times arguments and a suitable perturbed test functions approach which is adapted to consider the general regime $ε\neq δ$.