  We review the calculation of the solar axion flux from axion-photon and
axion-electron interactions and discuss the size of various effects neglected
in current calculations. For the Primakoff flux we then explicitly include the
partial degeneracy of electrons. We survey the available solar models and
opacity codes and develop a publicly available C++/Python code to quantify the
associated systematic differences and statistical uncertainties. The number of
axions emitted in helioseismological solar models is systematically larger by
about 5% compared to photospheric models, while the overall statistical
uncertainties in solar models are typically at the percent level in both
helioseismological and photospheric models. However, for specific energies, the
statistical fluctuations can reach up to about 5% as well. Taking these
uncertainties into account, we investigate the ability of the upcoming
helioscope IAXO to discriminate KSVZ axion models. Such a discrimination is
possible for a number of models, and a discovery of KSVZ axions with high $E/N$
ratios could potentially help to solve the solar abundance problem. We discuss
limitations of the axion emission calculations and identify potential
improvements, which would help to determine axion model parameters more
accurately.
