In a recent paper, with Drago and Pinamonti we have introduced a Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using the algebraic approach to perturbative QFT. The equation governs the flow of the average effective action, under changes of a mass parameter k. Here we introduce an analogous flow equation for gauge theories, with the aid of the Batalin-Vilkovisky (BV) formalism. We also show that the corresponding average effective action satisfies a Slavnov-Taylor identity in Zinn-Justin form. We interpret the equation as a cohomological constraint on the functional form of the average effective action, and we show that it is consistent with the flow.