Question

Can a neutrinos mass oscillate in a similar way to its flavour?

Answer 1

i.e. would it be possible for the flavour eigenstate of a quark/lepton produced in a weak interaction to be detected as a different flavour eigenstate at a distant detector due to the states propagating according to their mass eigenstates
The Cabibbo–Kobayashi–Maskawa (CKM) matrix mixes the flavor eigenstates of quar
CP violations mix d, s and b quarks and u, c and t quarks. The weak interaction partners of mass eigenstates of down type quarks d'. s' and b' are according to d, s and b and similarly up-type quarks, u′, c′ and t′, in terms of u, c, and t.

Answer 2

neutrinos can ‘oscillate’ or transmute from one kind (flavour) to another. But the rationale for why such an oscillation or change implies that neutrinos have mass.