Alloxazines are a promising class of organic electroactive compounds for application in aqueous redox flow batteries (ARFBs), whose redox properties need to be tuned further for higher performance. High-throughput computational screening (HTCS) enables rational and time-efficient study of energy storage compounds. We compared the performance of computational chemistry methods, including the force field based molecular mechanics, semi-empirical quantum mechanics, density functional tight binding, and density functional theory, on the basis of their accuracy and computational cost in predicting the redox potentials of alloxazines. Various energy-based descriptors, including the redox reaction energies and the frontier orbital energies of the reactant and product molecules, were considered. We found that the lowest unoccupied molecular orbital (LUMO) energy of the reactant molecules is the best performing chemical descriptor for alloxazines, which is in contrast to other classes of energy storage compounds, such as quinones that we reported earlier. Notably, we present a flexible in silico approach to accelerate both the singly and the HTCS studies, therewithal considering the level of accuracy versus measured electrochemical data, which is readily applicable for the discovery of alloxazine-derived organic compounds for energy storage in ARFBs.