Organ-on-chip (OoC) systems are microfluidic devices for maintaining live tissue under physiologically relevant (flow) conditions. Imaging of structure and flow is important for the characterization of OoC device design and visualizing tissue/fluid interaction. Here, we present 3D tissue and flow imaging in an OoC device with multi-modal optical coherence tomography (OCT) using a combination of OCT structural imaging and flow imaging with Doppler OCT, number fluctuation dynamic light scattering OCT, and particle image velocimetry OCT. We demonstrate the feasibility of combined imaging of OoC tissue culture morphology and high flow velocities. We also measure low velocities in the OoC tissue well showing good agreement with computational fluid dynamics simulations. Our results open up the way for studying the effect of flow on living tissue in OoC devices.