Magnetized hybrid nanofluid (HNF) flow across a spinning inclined disc (SID) under Thompson–Troian slip (TTS) conditions has numerous applications. It can help improve the efficiency of cooling systems in electrical appliances by optimizing lubricant flow and energy transportation. In the current work, we have studied the HNF flow over a SID under multiple slip conditions in the form of partial differential equations (PDEs). The black iron oxide (Fe3O4) or Iron (II, III) oxide, along with silver (Ag) nanoparticles (NPs), is mixed with vacuum pump oil (VPO) for the preparation of HNF. The fluid flow is investigated in relation to nonlinear heat radiation, viscous dissipation, mixed convection, Joule heating, and irregular heat source/sink. The system of PDEs is first converted into a non-dimensional form of ODEs and then solved numerically through the BVP4c technique. It has been determined that the flow rate of HNF (Ag and Fe3O4/VPO) declines with the variation of Ag and Fe3O4 NPs in VPO, and the magnetic field parameter. The fluid temperature distribution declines with the influence of NPs' volume friction. By varying the NPs volume friction (Ag and Fe3O4-NPs) from 0.01 to 0.03, the coefficient of Nusselt number (energy transfer rate) increases up to 31.6401%. Physically, Ag and Fe3O4 NPs in VPO have a high thermal conductivity, which more efficiently boosts the energy transfer rate and is more applicable to the cooling systems and energy transportation.