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Niobium chloride (Nb3Cl8) is a layered 2D semiconducting material with many exotic properties including a breathing kagome lattice, a topological flat band in its band structure, and a crystal structure that undergoes a structural and magnetic phase transition at temperatures below 90 K. Despite being a remarkable material with fascinating new physics, the understanding of its phonon properties is at its infancy. In this study, we investigate the phonon dynamics of Nb3Cl8 in bulk and few layer flakes using polarized Raman spectroscopy and density functional theory (DFT) analysis to determine the material's vibrational modes, as well as their symmetrical representations and atomic displacements. We experimentally resolved 12 phonon modes, 5 of which are A1g modes while the remaining 7 are Eg modes, which is in strong agreement with our DFT calculation. Layer-dependent results suggest that the Raman peak positions are mostly insensitive to changes in layer thickness, while peak intensity and FWHM are affected. Raman measurements as a function of excitation wavelength (473-785 nm) show a significant increase of the peak intensities when using a 473 nm excitation source, suggesting a near resonant condition. Temperature-dependent Raman experiments carried out above and below the transition temperature did not show any change in the symmetries of the phonon modes, suggesting that the structural phase transition is likely from the high temperature P3m1 phase to the low-temperature R3m phase. Magneto-Raman measurements carried out at 140 and 2 K between -2 to 2 T show that the Raman modes are not magnetically coupled. Overall, our study presented here significantly advances the fundamental understanding of layered Nb3Cl8 material which can be further exploited for future applications.