Microfluidic approaches to study tissue barriers have emerged to address the lack of fluid flow in conventional "open-well" Transwell™-like devices. However, microfluidic techniques have not achieved widespread usage in bioscience laboratories because they are not fully compatible with conventional tried-and-true experimental protocols. To advance barrier tissue research, there is a need for a platform that combines the advantages of both conventional open-well and microfluidic systems. Here, we develop a plug-and-play flow module to add on-demand microfluidic capabilities to a modular microfluidic system featuring a silicon membrane "m-μSiM" as an open-well device with live-cell imaging capabilities. The magnetic latching assembly of our design enables bi-directional reconfiguration between open-well and fluidic modes. This design feature provides users with the flexibility to conduct an experiment in an open-well format with established protocols and then add or remove microfluidic capabilities as desired. Our work also provides an experimentally-validated flow model to help select desired flow conditions based on the experimental needs. As a proof-of-concept, we demonstrate flow-induced alignment of endothelial cells and visualize different phases of neutrophil transmigration across an endothelial monolayer under flow. We anticipate that our reconfigurable design will be adopted by both engineering and bioscience laboratories due to the compatibility with standard open-well protocols and the simple flow addition capabilities.