Color centers in hexagonal boron nitride (hBN) have emerged as promising candidates for single-photon emitters (SPEs) due to their bright emission characteristics at room temperature. In contrast to mono- and few-layered hBN, color centers in multi-layered flakes show superior emission characteristics such as higher saturation counts and spectral stability. Here, we report a method for determining both the axial position and three-dimensional dipole orientation of SPEs in thick hBN flakes by tuning the photonic local density of states using vanadium dioxide (VO2), a phase change material. Emitters under study exhibit a strong surface-normal dipole orientation, providing some insight on the atomic structure of hBN SPEs, deeply embedded in thick crystals. We have optimized a hot pickup technique to reproducibly transfer flakes of hBN from VO2 onto SiO2/Si substrate and relocated the same emitters. Our approach serves as a practical method to systematically characterize SPEs in hBN prior to integration in quantum photonics systems.