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This study utilises mathematical modelling and computations to analyse the magnetohydrodynamic (MHD) effects on non-Newtonian Eyring–Powell fluid flow in an inclined non-uniform channel under long-wavelength, low Reynolds number conditions. The governing equations are solved by applying slip boundary conditions to determine the velocity, temperature, concentration, and streamline profiles. The key findings show that the magnetic parameter dampens the flow rate. The relationship between the variable viscosity, velocity, and temperature is nonlinear. The wall rigidity parameter and axial velocity are directly proportional until a threshold. Increasing inclination angles distorts streamlines. The magnetic field alters concentration contours and thermal transport. MATLAB parametric analysis explores MHD effects. This study enhances the understanding of inclined channel fluid dynamics, offering insights into variable viscosity, magnetic fields, wall properties, and impacts of inclination angles on non-Newtonian flow characteristics. This knowledge can optimise industrial MHD conduit/channel transport applications.