  We investigate neutrino flavor oscillations in vacuum within a general
conformal coupling model. We first examine the flavor oscillations within the
plane-wave description of neutrinos, and then we extend our analysis to the
wavepacket-based formalism. In both cases, we derive the general formulas for
the flavor transition probability in arbitrary static and spherically symmetric
spacetimes. We thoroughly discuss and assess in both cases the different
possible ways -- dictated by the presence of the conformal coupling -- of
computing the flavor transition probability. We show that the conformal
invariance of the Dirac equation implies that the effect of conformal coupling
on neutrino flavor oscillations modifies the oscillation length, but preserves
the coherence length and unitarity. A detailed application to two-flavor
neutrinos is then made and a numerical analysis is conducted within the
well-known chameleon conformal coupling model.
