Flow batteries are a compelling grid-scale energy storage technology because the stored energy is decoupled from the system power. Aqueous redox flow batteries (RFBs), however, are limited by low open-circuit voltages (OCVs). Replacing the aqueous negative electrolyte (negolyte) with liquid alkali metals—of which Na-K, a room-temperature liquid metal alloy, is attractive—would increase the OCV considerably. However, a suitable solid electrolyte has not been reported for Na-K. Here we show that K-β″-alumina is a selective and robust K+ ion conductor in contact with Na-K, to which it is stable with minimal exchange of Na. We report the cycling of cells with OCVs of 3.1–3.4 V employing aqueous and nonaqueous positive electrolytes (posolytes), and power density tests showing promising maximum power densities of 65 mW cm-2 at 22 ºC and >100 mW cm-2 at 57 ºC, ohmically limited by 330-um K-β″-alumina membranes. Further development of Na-K|K-β″-alumina batteries could unlock cost-effective energy storage.