The rational design and development of cost-effective, high-performance, and stable bifunctional oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) electrocatalysts are essential for rechargeable zinc-air batteries. Herein, a novel FeCo composite composed of alloy nanoparticles embedded in an N, S dual-doped carbon matrix (FeCo/NSC) was prepared via one-step carbonization of amphiphilic dodecanethiol-metal salts wrapped in carbon nitride (C3N4). The compact combination of dual metal-alloys and dual-doped carbon endowed the composite with the active sites for the ORR and OER, achieving efficient electrical transmission and highly efficient bifunctional catalytic performance. The obtained FeCo-1/NSC catalyst exhibited excellent electrocatalytic activity with a half-wave potential of 0.82 V (vs. RHE) for the ORR and a low overpotential of 0.325 V at 10 mA cm−2 for the OER. The liquid Zn-air battery with FeCo-1/NSC as an air electrode displayed excellent charge-discharge performance, high power density, and robust charge-discharge stability for 150 h compared to the 20% Pt/C + RuO2 counterpart. Furthermore, the FeCo-1/NSC-based flexible solid-state Zn-air battery exhibited a higher power density and good charge-discharge stability over 10 h of operation. Thus, a promising strategy for bifunctional electrocatalyst development as part of rechargeable and wearable Zn-air batteries was provided.