The feature of tunable constituents in covalent organic polymers (COPs) via combination of predesigned building units is of great interest in exploring multi-functional catalysts. Here, we report constituent-tunable metal-phthalocyanine-based covalent organic polymers as self-sacrificial precursors for fabrication of mono-(Fe or Ni) and bi-metallic (Fe-Ni) heteroatoms/carbon catalysts toward both oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). As a result, the as-prepared FeNi-COP-800 exhibits an efficient ORR performance with a half-potential of 0.80 V as well as an IrO2-like OER activity with a potential of 1.63 V at 10 mA cm(-2), which surpass those of monometallic Fe-COP-800 and Ni-COP-800. Moreover, a zinc-air flow battery using FeNi-COP-800 catalyst not only shows a higher power density than the battery using Pt/C-IrO2/C but also displays superior stability with 2.90% potential loss after 85 cycles in 175 h of practical operation. Accordingly, this work provides a facile but efficient approach in molecular incorporation of desired constituents to obtain bi/multi-active sites in a single catalyst for various catalytic roles, including, but not limited to, oxygen reduction, hydrogen evolution, oxygen evolution.