We investigate the EOF of a Powell-Eyring fluid through a slit microchannel, employing Navier slip boundary condition. Using an analytical scheme consistent with the homotopy perturbation method, we bring out the alteration in the underlying flow dynamics as attributable to the nonlinear interactions between fluid rheology and electrostatics over interfacial scales. We validate the approximate analytical solutions by comparing those with results from numerical analysis. We unveil a regime of phenomenal amplification in the net volumetric flow rate, realized as a consequence of an intricate interplay between interfacial electromechanics, slipping hydrodynamics, and the flow rheology. Our results may have far ranging consequences in the design of various biomicrofluidic devises/systems, which are often used for the manipulation of non-Newtonain fluids.