Chemical and structural diversity present in hexagonal boron nitride (h-BN) and graphene hybrid nanostructures provide avenues for tuning various properties for their technological applications. In this paper we investigate the variation of thermal conductivity (kappa) of hybrid graphene/h-BN nanostructures: stripe superlattices and BN (graphene) dots embedded in graphene (BN) are investigated using equilibrium molecular dynamics. To simulate these systems, we have parametrized a Tersoff type interaction potential to reproduce the ab initio energetics of the B-C and N-C bonds for studying the various interfaces that emerge in these hybrid nanostructures. We demonstrate that both the details of the interface, including energetic stability and shape, as well as the spacing of the interfaces in the material, exert strong control on the thermal conductivity of these systems. For stripe superlattices, we find that zigzag configured interfaces produce a higher kappa in the direction parallel to the interface than the armchair configuration, while the perpendicular conductivity is less prone to the details of the interface and is limited by the kappa of h-BN. Additionally, the embedded dot structures, having mixed zigzag and armchair interfaces, affect the thermal transport properties more strongly than superlattices. The largest reduction in thermal conductivity is observed at 50% dot concentration, but the dot radius appears to have little effect on the magnitude of reduction around this concentration.