All-solid-state rechargeable Zn-air battery is deemed to be a promising class of power source for its attractive operational safety and mechanical flexibility. To achieve high performance of Zn-air battery, the density of active sites on the ORR/OER bifunctional electrocatalyst and the maximized access to them are of great importance. In this study, a nitrogen, sulfur and ferric co-doped three-dimensional bifunctional catalyst (FeNx/N,S–C) is developed via a facile and eco-friendly molten salt assisted synthesis. The homogeneously dispersed FeNx species, the surrounding S dopants and the 3D hierarchical architecture synergistically endow FeNx/N,S–C with dense active sites with high accessibility, abundant open pores/channels and efficient mass transfer. Compared with the commercial Pt/C–RuO2 catalyst, the application of FeNx/N,S–C in all-solid-state rechargeable Zn-air batteries results in enhanced ORR/OER activities, lower charge-discharge voltage gaps and improved 52 h cycling durability, implying its good feasibility in practical application. The all-solid-state FeNx/N,S–C based battery shows no performance decay during charge-discharge cycles when its sodium polyacrylate hydrogel electrolyte is compressed up to 67% strain or stretched up to 400% length, implying the feasibility of the present FeNx/N,S–C catalyst in the usage of stable and flexible electronics.