We compute the Picard group of the moduli stack of genus zero stable quotients to projective space, Grassmannians, and any SL flag variety in the case of more than 2 markings. Furthermore, in the case of exactly 2 markings, we calculate the Picard group of the moduli stack of genus zero stable quotients to projective space, Grassmannians, and to partial flag varieties where the ranks of the subspaces differ by more than 1. Along the way we establish projectivity of the coarse moduli space.