Redox flow batteries are widely investigated toward cost-effective storage of energy generated via intermittent renewable sources. Many redox chemistries have been proposed for flow batteries, possessing various attractive features such as low-cost reactants, fast electrochemical reaction kinetics without precious metal catalysts, negligible thermal runaway risk, and low toxicity. While all flow batteries rely on heterogeneous electrochemical reactions occurring at electrode surfaces, in a subset of chemistries homogeneous chemical reactions occur in the electrolyte. A prominent example are batteries employing halogen-based catholytes, where halogen molecules complex with halide ions in the catholyte, forming redox-active polyhalide ions. However, state-of-the-art models capturing flow battery performance for halogen systems typically neglect the presence of such homogeneous reactions and polyhalide ions. The latter assumption allows for simpler models, but at the cost of accurately predicting battery chemical state and performance. We here present a generalized flow battery theory extended to include fast homogeneous reactions, which employs a technique known as the method of families to simplify the governing equations. We then apply and solve the model for the specific case of a membraneless hydrogen-bromine flow battery, illustrating the predicted effect of the homogeneous complexation reaction in the catholyte on flow battery performance.