NbRe, a non-centrosymmetric superconductor with a transition temperature Tc up to 9 K, attracts interest for its strong antisymmetric spin-orbit coupling and suitability for single-photon detection. While bulk and thin-film polycrystalline NbRe are well studied, how superconductivity and vortex dynamics evolve with increasing grain size in thin films is largely unknown. Here, we investigate as-grown and annealed 20 nm-thick NbRe films, where annealing increases the average crystallite size from approximately 2 nm to 8 nm, and study vortex dynamics via current-voltage (I-V) measurements over a broad temperature and magnetic field range. In contrast to as-grown films, where the low-resistive state breaks down due to flux-flow instability, annealed films exhibit multiple voltage kinks in the I-V curves. We attribute these kinks to the nucleation and growth of normal domains, as further suggested by time-dependent Ginzburg-Landau simulations. Overall, the annealed films form superconducting networks with vortex-channeling paths along the grain boundaries, while localized heating and voltage kinks could be harnessed for discrete-resistance switching and sensing.