  Neutrino propagation in the Galactic magnetic field is considered. To
describe neutrino flavour and spin oscillations on the galactic scale baselines
an approach using wave packets is developed. Evolution equations for the
neutrino wave packets in a uniform and non-uniform magnetic field are derived.
Analytical expressions for neutrino flavour and spin oscillations probabilities
accounting for damping due to wave packet separation are obtained for the case
of uniform magnetic field. It is shown that for oscillations on magnetic
frequencies $\omega_i^B = \mu_i B_\perp$ the coherence lengths that
characterizes the damping scale is proportional to the cube of neutrino average
momentum $p_0^3$. Probabilities of flavour and spin oscillations are calculated
numerically for neutrino interacting with the non-uniform Galactic magnetic
field. Flavour compositions of high-energy neutrino flux coming from the
Galactic centre are calculated accounting for neutrino interaction with the
magnetic field. It is shown that for neutrino magnetic moments $\sim 10^{-13}
\mu_B$ and larger these flavour compositions significantly differ from ones
predicted by the vacuum neutrino oscillations scenario.
