  In this work, we study the propagation of high energy neutrinos produced in
extragalactic sources including the effect of a possible interaction with
ultralight axion-like particles (UALP) with a mass $m_a\sim 10^{-22} {\rm eV}$
as the constituents of dark matter (DM) under the assumption that their
coupling to neutrinos is dominant. We compute the cross section and describe
the propagation of a diffuse neutrino flux using transport equations for each
mass eigenstate. This allows us to obtain the neutrino fluxes of the different
flavors to be observed at the Earth with neutrino telescopes under different
assumptions for the flavor composition emitted at the sources and for a normal
ordering (NO) or an inverted ordering (IO) of the neutrino masses. If the
coupling of neutrinos with UALPs is the same for all flavors ($g_{\nu a}$), we
find that interactions change the flavor composition of neutrinos arriving on
Earth for $g_{\nu a}\gtrsim 0.5\,{\rm GeV}^{-1}$, causing the electron(muon)
flavor to dominate in the NO(IO) case for neutrino energies above $\sim
10^5\,{\rm GeV}$. Although current data on the flavor ratios suggest that
interactions with UALP DM do not take place within the range of coupling
studied (particularly in the NO case) more data is needed to improve the
precision of the experimentally measured flavor composition.
