Jeffrey fluid flow past an inclined stretchable sheet affected by magnetic dipole and suction/injection was investigated. The applicable equations were changed into nonlinear ordinary differential equations by similarity transformations. With the Chebyshev spectral collocation approach, solutions were obtained for fluid velocity and temperature. Considering the prescribed surface temperature (PST) and prescribed heat flux (PHF) heat processes, the effect of inclination angle, the Grashof number, and other parameters on the velocity and temperature of the fluid were documented by graphs and tables. Without the angle of inclination, the solutions from this work were found to agree with those of the Generic algorithm and Nelder Mead method. The fluid is slower when the plate is inclined at a larger angle and this tends to allow for higher fluid temperature. The ferromagnetic interaction parameter and the ratio of relaxation to retardation time have the same effect on fluid velocity and temperature as the angle of inclination. The suction parameter and Prandtl number amplify the Nusselt number, while as the suction increases the skin friction increases for all inclination angles. With these results, engineers in chemical/polymer industries can make the appropriate changes which can lead to more quality production.