We consider Anosov subgroups of a semi-simple Lie group, a higher rank generalization of convex cocompact groups. Cocompact domains of discontinuity for these groups in flag manifolds were constructed systematically by Kapovich, Leeb and Porti in [KLP18]. For ∆-Anosov groups, we show that every cocompact domain of discontinuity arises from this construction, up to a few exceptions in low rank. We use this to compute which flag manifolds admit such domains, and the number of different domains in some cases. We also find a new compactification for locally symmetric spaces arising from maximal representations into Sp(4n+2,R).