An important class of electrokinetic, microfluidic devices aims to pump and control electrolyte working liquids that have spatial gradients in conductivity. These high-gradient flows can become unstable under the application of a sufficiently strong electric field. In many of these designs, flow channels are thin in the direction orthogonal to the main flow and the conductivity gradient. Viscous stresses due to the presence of these walls introduce a stabilizing force that plays a major role in determining the overall instability. A thin channel model for fluid flow is developed and shown to provide good agreement with a complete three-dimensional model for channel aspect ratios less than or similar to 0.1.