Quantum emitters based on atomic defects in layered hexagonal Boron Nitride (hBN) have emerged as promising solid state 'artificial atoms' with atom-like photophysical and quantum optoelectronic properties. Similar to other atom-like emitters, defect-phonon coupling in hBN governs the characteristic single-photon emission and provides an opportunity to investigate the atomic and electronic structure of emitters as well as the coupling of their spin- and charge-dependent electronic states to phonons. Here, we investigate these questions using photoluminescence excitation (PLE) experiments at T=4K on single photon emitters in multilayer hBN grown by chemical vapor deposition. By scanning up to 250 meV from the zero phonon line (ZPL), we can precisely measure the emitter's coupling efficiency to different phonon modes. Our results show that excitation mediated by the absorption of one in-plane optical phonon increases the emitter absorption probability ten-fold compared to that mediated by acoustic or out-of-plane optical phonons. We compare these measurements against theoretical predictions by first-principles density-functional theory of four defect candidates, for which we calculate prevalent charge states and their spin-dependent coupling to bulk and local phonon modes. Our work illuminates the phonon-coupled dynamics in hBN quantum emitters at cryogenic temperature, with implications more generally for mesoscopic quantum emitter systems in 2D materials and represents possible applications in solid-state quantum technologies.