Strongly coupled light-matter systems can carry information over long distances and realize low-threshold polariton lasing, condensation, and superfluidity. These systems are highly nonequilibrium in nature, so constant nonzero fluxes manifest themselves even at the steady state and are set by a complicated interplay between nonlinearity, dispersion, pumping, dissipation, and interactions between the various constituents of the system. Based on the mean-field governing equations of lasers or polariton condensates, we develop a method for engineering and controlling the velocity profiles by manipulating the spatial pumping and dissipation in the system. We present analytically exact pumping and dissipation profiles that lead to a large variety of spatially periodic density and velocity profiles. Besides these, any physically relevant velocity profiles can be engineered by finding the stationary state of the conservative nonlinear Schrödinger equation in an external potential related to the velocity. Our approach opens the way to the controllable implementation of laser or polariton flows for ultrafast information processing, integrated circuits, and analog simulators.