Cells use 'active' energy-consuming motor and filament protein networks to control micrometre-scale transport and fluid flows. Biological active materials could be used in dynamically programmable devices that achieve spatial and temporal resolution that exceeds current microfluidic technologies. However, reconstituted motor-microtubule systems generate chaotic flows and cannot be directly harnessed for engineering applications. Here we develop a light-controlled programming strategy for biological active matter to construct micrometre-scale fluid flow fields for transport, separation and mixing. We circumvent nonlinear dynamic effects within the active fluids by limiting hydrodynamic interactions between contracting motor-filament networks patterned with light. Using a predictive model, we design and apply flow fields to accomplish canonical microfluidic tasks such as transporting and separating cell clusters, probing the extensional rheology of polymers and giant lipid vesicles and generating mixing flows at low Reynolds numbers. Our findings provide a framework for programming dynamic flows and demonstrate the potential of active matter systems as an engineering technology.