This work analyzes the pressure driven flow of a power law fluid in a slit microchannel of asymmetric walls with electroviscous effects. The steady state Cauchy momentum and the Poisson-Boltzmann equation are solved for the velocity and the potential distribution inside the microchannel. The Debye-Huckel approximation as applicable for low zeta potentials is not made in the present work. The unknown streaming potential is solved by casting the governing equations as an optimization problem using COMSOL Multiphysics. This proposed method is very robust and can be used for a wide variety of cases. It is found that the asymmetry of the zeta potential at the two walls plays an important role on the streaming potential developed. There is a unique zeta potential ratio at which the streaming potential exhibits a maxima for both Debye-Huckel parameter and the power law index. Shear thinning fluids exhibit a stronger dependency of the streaming potential on asymmetry of the zeta potential than shear thickening fluids. For Newtonian fluids narrow slit microchannels develop larger streaming potentials compared to wider microchannels for a given asymmetry.