Summary: An analytical investigation is conducted to analyze the impact of magnetic field and hydrodynamic slippage on two-dimensional electro-osmotic Brinkman flow in a microchannel with cosine surface zeta potential. The Brinkman equation is utilized to govern the fluid flow within a fully saturated, homogeneous, and isotropic porous medium. We consider a very small magnetic Reynolds number to eliminate the induced magnetic field equation. The Navier slip boundary condition is applied to assess the impact of hydrodynamic slippage. We utilize the Debye-Huckel length approximation to linearize the Poisson-Boltzmann equation, which governs the potential of the electrical double layer. The stream function is obtained analytically, and contour plots, velocity fields, shear stresses, and pressure gradients are assessed to gain a proper understanding of flow physics. We utilize the stream function to plot the streamline plots for distinct assumed flow parameters. We observed that for a fixed Darcy number, the intensity of flow vortices decreases with increasing Hartman number while increasing with increasing slip length. Further, altering the wave number in the assumed cosine-waved zeta potential causes asymmetrical recirculations in the flow, which helps in increasing the scalar mixing process in microdevices. Further, the proposed investigation has various crucial applications, such as microfluidic cooling systems, drug delivery systems, and so on.