  Under the main assumption that the axion scalar field mainly composes the
dark matter in the Universe, in this paper we shall extend the formalism of
kinetic axion $R^2$ gravity to include Gauss-Bonnet terms non-minimally coupled
to the axion field. As we demonstrate, this non-trivial Gauss-Bonnet term has
dramatic effects on the inflationary phenomenology and on the kinetic axion
scenario. Specifically, in the context of our formalism, the kinetic axion
ceases to be kinetically dominated at the end of the inflationary era, since
the condition $\dot{\phi}\simeq 0$ naturally emerges in the theory. Thus,
unlike the case of kinetic axion $R^2$ gravity, the Gauss-Bonnet corrected
kinetic axion $R^2$ gravity leads to an inflationary era which is not further
extended and the reheating era commences right after the inflationary era,
driven by the $R^2$ fluctuations.
