We simulate flow into and through a nascent colloidal superlattice using an equivalent network model. By distilling the constitutive equations for creeping flow through complex geometries, the network model enables one to describe key features of the colloidal assembly: packing selectivity, particle convection and growth rates, boundary facets, and capillary pressure distribution. Simulations of evaporation-driven flow in close-packed colloidal superlattices of nearly monodisperse spheres are presented. Selectivity for face-centered cubic packing through a (111) growth facet is discussed, as is solvent flow through (100), (110), and (311) planes. Differences amongst these boundary arrangements are shown to dictate the distribution of liquid amongst the available pore throats, while not influencing the total convective flux. This ambiguity in the model is eliminated using a volume-averaged material balance to identify the appropriate physical and geometric parameters. Employing such a material balance alongside the network model itself, one can estimate the convective flux and hence growth rates and capillary pressure distributions. The analogous electrical network model addresses the fundamental question of crystal structure selectivity and boundary facet shapes.