Flexible rechargeable zinc–air batteries are considered as one of the most promising power supplies for the emerging flexible and wearable electronic devices. However, the development of flexible zinc–air batteries is stagnant due to the lack of efficient bifunctional catalysts with high oxygen catalytic activity and flexible solid‐state electrolytes with high mechanical stability and ionic conductivity. In this work, Co3O4/Ag@NrGO composite was synthesized by a facile one‐pot method, and the catalyst shows remarkable oxygen reduction reaction (ORR)/oxygen evolution reaction (OER) bifunctional catalytic activity and good long‐term stability. In particular, the OER overpotential of Co3O4/Ag@NrGO reaches 437 mV, outperforming that of the commercial IrO2 catalyst. This can be attributed to the combined effects of Co3O4, Ag, and N‐rGO. Furthermore, PAA (polyacrylic acid) and PVA (polyvinyl alcohol) based gel‐electrolytes have been developed as flexible solid‐state electrolytes for zinc–air batteries. The results show that PAA‐based electrolyte is more favorable to the flexible zinc–air battery with a high power density due to its relatively high ionic conductivity. The maximum power density of flexible zinc–air batteries with Co3O4/Ag@NrGO catalyst and PAA‐based electrolyte can reach 108 mW cm−2, which is almost the highest value reached in recent reports. This work will provide valuable guidance for the development of flexible rechargeable zinc–air batteries with high power density and stability.