The Sun is a source of high energy neutrinos (E > 10 GeV) produced by cosmic ray interactions in the solar atmosphere. We study the impact of three-flavor oscillations on the solar atmosphere neutrino fluxes observable at Earth. We find that peculiar matter oscillation effects in the Sun do exist, but are significantly suppressed by averaging over the production region and over the neutrino and antineutrino components. In particular, the relation between the neutrino fluxes at the Sun and at the Earth can be approximately expressed in terms of phase-averaged ''vacuum'' oscillations, dominated by a single mixing parameter (the angle {theta}{sub 23}).