Developing highly active, cost‐effective, and durable bifunctional oxygen electrocatalysts is an important step for the advancement of rechargeable Zn–air batteries (ZABs). Herein, an efficient bifunctional oxygen electrocatalyst of ultrathin Co(OH)2 nanosheets supported on nitrogen‐doped carbon nanoflake arrays (named as Co(OH)2@NC), is reported, which yields excellent bifunctional activity, i.e., a low overpotential of 285 mV to reach 10 mA cm−2 for oxygen evolution reaction (OER), a high half‐wave potential (0.83 V) for oxygen reduction reaction (ORR), and a low potential gap (ΔE) of 0.69 V. The excellent bifunctional catalytic performance can be ascribed to the concerted efforts of cobalt hydroxide toward OER and nitrogen‐doped carbon for ORR. The Co(OH)2@NC nanoflake arrays is further used as binder‐free air cathodes for rechargeable Zn–air batteries, exhibiting a high specific capacity of 798.3 mAh gZn−1, improved stability (a working life of >70 h at 5 mA cm−2), as well as a reduced long‐term charging voltage, which outperforms the counterparts of NC nanoflake arrays and Pt/C‐based air cathodes. One step further, the Co(OH)2@NC nanoflake arrays on carbon cloth are directly used as binder‐free air cathodes for flexible, solid‐state ZABs, showing excellent performance under deformation as well.