This paper examines the thermally radiative Poiseuille flow of a non-Newtonian Jeffrey fluid through a porous medium with variable inclination and permeability. For simplification, let us assume that permeability varies in a quadratic parabolic form. The Brinkman model is applied to the porous medium to effectively regulate the flow. The impacts of viscous dissipation are also incorporated into the energy equation. The exact solution for velocity and temperature fields is obtained using the direct integration method, and then the obtained results are plotted to see the influence of different physical parameters. Furthermore, the skin friction coefficient and local Nusselt numbers are precisely calculated numerically for a variety of parameters, with the results presented comprehensively in tabular form. It is observed that the maximum permeability of the porous medium affects both the mass flow rate and the velocity, which increase with rising Jeffrey and decrease with rising Hartmann, number, respectively.