This study examines the unsteady magnetohydrodynamic (MHD) flow of a second-grade viscoelastic fluid between vertical parallel plates, incorporating thermal radiation, non-uniform heat source/sink, and chemically reactive species. The governing equations for momentum, energy, and mass transfer account for temperature-dependent properties, Joule heating, viscous dissipation, and cross-diffusion effects, with radiative heat flux modeled via the Rosseland approximation. An applied transverse magnetic field induces Lorentz forces, while the second-grade fluid model captures viscoelastic memory effects. The coupled nonlinear system is solved analytically for small oscillations using perturbation methods and numerically via a Crank-Nicolson finite difference scheme for general cases. Parametric analysis reveals that thermal radiation (Rd > 1) increases thermal boundary layer thickness by 18–25%, while Joule heating elevates temperatures by 12–20%. The viscoelastic parameter (β = 0.1–0.5) delays flow stabilization by 30–50% compared to Newtonian fluids, and chemical reactions (Da > 0.5) reduce species concentration by 15–40% while enhancing thermal stratification through reactive heating/cooling. Magnetic fields (Ha > 5) suppress velocity oscillations by 35–60%, promoting flow stability. These findings demonstrate strong coupling between radiative heat transfer, MHD effects, and reaction kinetics in viscoelastic flows, with direct implications for nuclear reactor cooling systems, polymer processing equipment, and energy-efficient thermal devices where controlled heat and mass transfer under magnetic fields are critical. The study provides a validated theoretical framework for optimizing such systems through tailored manipulation of radiative, magnetic, and rheological parameters.