Cholesteric liquid crystals (CLCs) are compelling responsive materials with applications in next-generation sensing, imaging, and display technologies. While electric fields and surface treatments have been used to manipulate the molecular organization and, subsequently, the optical properties of CLCs, their response to controlled fluid flow has remained largely unexplored. Here, we investigate the influence of microfluidic flow on the structure of thermotropic CLCs that can exhibit structural coloration. We demonstrate that the shear forces that arise from microfluidic flow align the helical axis of CLCs; alignment is a prerequisite for harnessing the promising photonic properties of CLCs. Moreover, we show that microfluidic flow can generate non-equilibrium structures exhibiting photonic band gaps that are inaccessible in the stationary cholesteric phase. Our findings have implications for the use of CLCs in applications involving flow processing such as additive manufacturing.