The migration of cells such as leukocytes, tumor cells, and fibroblasts through 3D matrices is critical for regulating homeostasis and immunity and for driving pathogenesis. Interstitial flow through the extracellular matrix, which can substantially increase during inflammation and in the tumor microenvironment, can influence cell migration in multiple ways. Leukocytes and tumor cells are heterogeneous in their migration responses to flow, yet most 3D migration studies use endpoint measurements representing average characteristics. Here we present a robust new microfluidic device for 3D culture with live imaging under well-controlled flow conditions, along with a comparison of analytical methods for describing the migration behavior of heterogeneous cell populations. We then use the model to provide new insight on how interstitial flow affects MDA-MB-231 breast cancer cell invasion, phenomena that are not seen from averaged or endpoint measurements. Specifically, we find that interstitial flow increases the percentage of cells that become migratory, and increases migrational speed in about 20% of the cells. It also increases the migrational persistence of a subpopulation (5-10% of cells) in the positive or negative flow direction. Cells that migrated upstream moved faster but with less directedness, whereas cells that migrated in the direction of flow moved at slower speeds but with higher directedness. These findings demonstrate how fluid flow in the tumor microenvironment can enhance tumor cell invasion by directing a subpopulation of tumor cells in the flow direction; i.e., towards the draining lymphatic vessels, a major route of metastasis.