The present study examines the effect of radiation and inclined magnetic field on the biviscosity Bingham hybrid nanofluid flow on the permeable stretching/shrinking surface. Hybrid nano fluid composites are formed by dissolving Graphene oxide (GO) and Molybdenum disulfide (MoS2) in base fluid Ethylene Glycol (EG), applying these nanoparticles to the Ethylene Glycol (base fluid) will enhance heat transfer. Furthermore, it studied the heat transmission process using variable thermal conductivity of the heat source/sink. Governing equations of velocity and temperature are converted to a set of nonlinear ordinary differential equations (ODE) via suitable transformations and the obtained equations are solved using the boundary conditions, energy equation with radiation, and heat source/sink effect solved analytically by using hypergeometric function. Significant physical characteristics like mass transpiration, Prandtl number, Biot number, and thermal radiations can be discussed using the graphical analysis. The investigation outcomes reveal that increasing the magnetic field enhances skin friction. Increasing the volume fraction, Biot number, and thermal radiation increases the thermal boundary layer, and velocity decreases by increasing the inverse Darcy parameter. Current work has many useful applications in engineering, biological and physical sciences, cleaning engine lubricants, thrust bearing technologies, etc.