The Analytical Transport Network (ATN) model was developed to study transport through heterogeneous and hierarchical microstructural networks. Here, ATN is extended to electrokinetic flow, a linear, coupled flow that satisfies Onsager's reciprocity relations. In Part 1, a channel-scale model was developed to describe electrokinetic flow through a channel of arbitrary morphology. In Part 2, we exploit the computational economy of the channel-scale model to develop an efficient network-scale model of electrokinetic flow in large, geometrically complex material structures. The corresponding algorithm for applying the theory to voxel-based, 3-D images is automated and computationally efficient. In addition, it provides a means for rapidly obtaining a structure's tortuosity factor from a 3-D image. We outline the manner in which morphology and topology exerts an additional influence on electrokinetic flow relative to pure conduction and viscous fluid flow. The effort represents an important initial step in extending the ATN approach to a broader range of linear and eventually nonlinear coupled flow phenomena. The extension is relevant to a number of technological fields, including emerging energy conversion and storage technologies.