Massive particles whose dynamics are described by the free Dirac equation can oscillate between left and right-handed chiral states, undergoing chiral oscillations. The phenomenon is prominent for non-relativistic particles, and can yield a depletion on the expected measured flux of cosmic neutrinos and a modification of quantum correlations encoded in lepton-antineutrino pairs. In this context, the interplay between chiral and flavor oscillations plays an important role in the description of neutrino flavor dynamics. In this paper, we extend previous results and obtain flavor oscillation formulas including chiral oscillations for $N$ flavor mixing. We consider the general case of mixing that can distinguish between left and right-handed states and derive the flavor oscillation probabilities for Dirac and Majorana neutrinos within the bispinor formalism. We show that, for three flavors, oscillation probabilities between chiral left and right-handed flavor states allows for distinguishing between Dirac and Majorana neutrinos in the presence of additional CP-violation Majorana phases. To summarize, our work addresses to phenomenologically accessible chiral oscillation effects on non-relativistic neutrino dynamics and on quantum correlations encoded in flavor states.