Endothelial cells (ECs) line the interior of blood and lymphatic vessels and experience spatially varying wall shear stress (WSS) as an intrinsic part of their physiological function. How ECs, and mammalian cells generally, sense spatially varying WSS remains poorly understood, due in part to a lack of convenient tools for exposing cells to spatially varying flow patterns. We built a multiplexed device, termed a 6-well impinging flow chamber, that imparts controlled WSS gradients to a six-well tissue culture plate. Using this device, we investigated the migratory response of lymphatic microvascular ECs, umbilical vein ECs, primary fibroblasts, and epithelial cells to WSS gradients on hours to days timescales. We observed that lymphatic microvascular ECs migrate upstream, against the direction of flow, a response that was unique among all the cells types investigated here. Time-lapse, live cell imaging revealed that the microtubule organizing center relocated to the upstream side of the nucleus in response to the applied WSS gradient. To further demonstrate the utility of our device, we screened for the involvement of canonical signaling pathways in mediating this upstream migratory response. These data highlight the importance of WSS magnitude and WSS spatial gradients in dictating the cellular response to fluid flow.