Polymer membranes containing selectively permeable flakes will show selective fluxes. If the flakes are highly selective, the relative fluxes will be proportional to the square root of the inherent selectivity. If the flakes are modestly selective, the relative fluxes may approach this more modest value. Achieving this selectivity requires carefully adjusting the diffusion coefficient in the polymer continuum to the geometric average of the diffusion coefficients in flakes times the aspect ratio of the flakes. These results are compared with other theories of composite membranes.