This study investigates the effects of chemical reactions and viscous dissipation on the magnetohydrodynamic (MHD) squeezing flow of a non-Newtonian Jeffrey fluid confined between two parallel plates with velocity slip boundary conditions. Squeezing flows of this type are of significant practical importance in industrial and engineering processes such as lubrication systems, polymer extrusion, ink-jet printing, and biomedical applications involving fluid transport through narrow gaps. The governing nonlinear partial differential equations are reduced to a system of ordinary differential equations using similarity transformations and solved numerically via the Runge–Kutta method, implemented through the MPALE computational code. Validation of the results through comparison with previously published studies shows excellent agreement with key parameters such as the skin friction coefficient, Nusselt number, and Sherwood number. The results reveal that wall shear stress and axial fluid velocity increase as the plates move toward each other, intensifying the squeezing effect. An increase in the magnetic parameter and in the ratio of relaxation to retardation times leads to a reduction in velocity, temperature, and concentration. Viscous dissipation is found to enhance the temperature distribution and increase the heat transfer rate. Regarding mass transport, species-generating chemical reactions reduce the mass transfer rate, whereas species-consuming (destructive) reactions increase it.