  We explore the generation of fermion masses and quark mixing angles within
flavored gauge mediation models of supersymmetry breaking in which the Higgs
and messenger doublets are connected by a discrete non-Abelian symmetry. In
this framework, the Higgs-messenger symmetry, which we take for concreteness to
be the discrete group $\mathcal{S}_3$, also plays the role of a (partial)
family symmetry. We investigate mechanisms for generating mass hierarchies for
the lighter quark generations and generating the Cabibbo angle within this
class of models. While perturbations of the couplings at the renormalizable
level do not lead to phenomenologically viable quark mixing parameters, we show
that the Cabibbo angle can be generated via couplings at the nonrenormalizable
level and explore the phenomenological implications of this scenario.
