We develop a formal analogy between configurational stresses in physically distinct systems, and study the flows that they induce when the configurations of interest include topological defects. Our primary focus is on electrokinetic flows in a nematic fluid under an applied electrostatic field, which we compare with a class of systems in which internal stresses are generated due to configurational changes (e.g., active matter, liquid crystal elastomers). The mapping allows the extension, within certain limits, of existing results on transport in electrokinetic systems to active transport. We study motion induced by a pair of point defects in a dipole configuration, and steady rotating flows due to a swirling vortex nematic director pattern. The connection presented allows the design of electrokinetic experiments that correspond to particular active matter configurations that may be easier to conduct and control in the laboratory.