This study reports the three-dimensional (3D) flow of Ag-MgO hybrid nanofluid (HNF) over a spinning disc of flexible thickness in the presence of modified Fourier law. The HNF is contained of silver and magnetic nanoparticulate in the base fluid engine oil. The energy transition has been examined in the involvement of melting heat propagation. The highly nonlinear system of partial differential equations (PDEs) is processed by adopting the proper similarity conversions to attain the coupled ODE system. The obtained system of modeled equations is numerically solved by employing the Parametric Continuation Method (PCM). The nature of various constraints, as opposed to the velocities, energy, and mass transmission, is portrayed and described. In comparison to the simple nanofluid flow, the hybrid nanoliquid flow’s velocity and heat conduction are observed to have a significant influence. As a result, the functionality of the hybrid nanoliquid is significantly superior to that of the conventional nanofluid. The positive variation in power-law exponent and Reynold number significantly enhances the fluid velocity. The effect of both melting coefficient and thermal relaxation term reduces fluid temperature.