This investigation focuses on the flow reversal and separation of hybrid nanofluid, with heat generation and first-order velocity slip, in a Darcy porous medium. The Choi–Eastman nanofluid model is used to formulate the hybrid nanofluid mathematical model. Suitable similarity transformations convert partial differential equations into a system of ordinary differential equations. The resultant systems are numerically solved by implementing the shooting approach. Multiple solutions are found for this current problem, and intriguingly, the velocity and temperature profiles of these two solution branches exhibit opposing characteristics. In conclusion, conducting a stability study on these two alternative solutions is worthwhile to determine which solution is more realistic and stable. The temporal stability test reveals that only the first solution is stable or physically valid. The important outcomes of this study, based on the stable solutions, are as follows: (i) the hybrid nanofluid’s Nusselt number, skin friction, and velocity rise when the inclined magnetic parameter rises, (ii) the value of the smallest eigenvalue increases with higher values of the inclined magnetic parameter, and (iii) the thickness of momentum and thermal boundary layers is thinner for the first solution than the second solution. Additionally, the identification of flow separation and reversal points is valuable for aerospace technology, following the Prandtl theory. Finally, this study provides streamlined patterns to enhance the understanding of fluid flow behavior.