This study presents a semi-analytical model for transient magnetohydrodynamic (MHD) flow with electrokinetic coupling in cylindrical capillaries representing subsurface oil transport pathways. The model incorporates Lorentz force, electric double layer (EDL) effects, constant pressure gradient, and time-dependent momentum in the Navier–Stokes equations. Using the electrokinetic potential and magnetic field parameters, the governing equations are transformed into a Bessel-type form and solved through Laplace transform methods. Analytical expressions for velocity, shear stress, and flow rate are obtained in Laplace domain after which a numerical inversion method based on Riemann-Sum Approximation is used to describe the flow behavior under combined magneto-electrohydrodynamic effects in time domain. Parametric results show that stronger magnetic fields damp velocity oscillations, while higher electrokinetic coupling enhances near-wall fluid motion due to EDL-induced slip. The interaction between magnetic field and electroosmotic forces determines the time required for full flow development. The findings provide insight into microscale transport in oil–brine mixtures and indicate that electrokinetic effects significantly increase both velocity and mass flow rate.