There is an analogy of Chow's lemma for a DM stack $X$ written in the Laumon's book 'Champ algebrique'. There exists a generically finite, proper surjective morphism $Y \to X$ from a quasi-projective scheme $Y$. Furthermore, assume that there be a connected linear algebraic group $G$ acts on $X$. Then, is there a such quasi-projective scheme $Y$ with $G$-action, and an equivariant morphism $Y \to X$?