<p>Electroosmotic flow (electric field induces fluid flow) has modernized the fluid dynamics by enabling precise control over fluid flow at the microscale and explored the new domain of technology i.e., microfluidics-based technology or lab-on-chip devices. This paper studies the membrane pumping-driven electroosmotic flow of non-Newtonian fluids in inclined microchannels where the non-Newtonian nature of fluid is defined by the Casson fluid model. The propagating membrane exhibits rhythmic contractions and relaxations over time. The governing equations are simplified using the lubrication approach, low Reynolds number approximation, and Debye–Hückel linearization, and derived the analytical solutions with the appropriate boundary conditions. The velocity profile, pressure gradient, pumping characteristics, wall shear stress, and stream function are analyzed with respect to key parameters, including the inclination angle, Casson fluid parameter, Helmholtz–Smoluchowski velocity, electroosmotic parameter, zeta potential, Reynolds number, and Froude number. The results reveal that the axial velocity and the pressure difference increase with the Casson fluid parameter, inclination angle, electroosmotic forces, and membrane shape, but decrease with Froude number. Conversely, the pressure gradient enhances with Froude number and declines with other parameters. Stream function magnitude intensifies with increasing inclination angle, Casson fluid parameter, Helmholtz-Smoluchowski velocity, zeta potential, and Reynolds number. These findings enhance the understanding of electroosmotic transport in complex fluids and support the design of efficient microfluidic systems for biomedical, chemical, and micro/nano-technological applications requiring precise flow control.</p>