Development of non-precious metal based oxygen electrocatalysts, particularly bifunctional ones for both oxygen reduction and oxygen evolution is at the heart of electrochemical energy research. Layered double hydroxides have great promise, and to fulfill their full potentials requires effective strategies to engineer and stabilize their structures at the nanoscale. In this study, we report the scalable preparation and delamination of atomic-thick CoNi layered double hydroxide nanosheets, and the subsequent flocculation from their colloidal dispersion upon the introduction of negatively charged graphene oxide nanosheets. Thanks to the large surface areas of CoNi layered double hydroxide monolayers and the high electrical conductivity of reduced graphene oxide support, the thus-formed composite exhibits bifunctional activity and stability far more superior to its close competitors for oxygen reduction and oxygen evolution in both 1 M and 6 M KOH. It could also be used as the oxygen electrocatalyst of rechargeable Zn-air batteries to enable remarkable discharge peak power density and stable cycling stability.