Gravitational waves provide a novel way to probe axions or axion-like particles coupled to a dark photon field, even in the absence of couplings to Standard Model particles. In the conventional misalignment mechanism, the generation of an observable stochastic gravitational wave background, however, requires large axion decay constants. We here investigate the gravitational wave signal generated within the kinetic misalignment scenario, where the axion is assumed to have a large initial velocity. Its kinetic energy then provides a sufficiently high energy budget to generate a detectable gravitational wave signal also at lower values of the decay constant. We obtain an analytic estimate as well as perform numerical simulations of the corresponding gravitational wave signal, and evaluate its detectability at current and future gravitational wave observatories. We further present the corresponding projected constraints on the parameter space of the model, along with the parameter regions in which the dark photon or axion constitute dark matter, or in which the baryon asymmetry of the Universe is generated via the axiogenesis mechanism. Finally, we compute the GW production from the fragmentation of rotating axions, which is however difficult to observe experimentally.