Basic requirements for advanced and practical supercapacitors need electrode materials with strong stability, high surface area, well-defined porosity, and enhanced capability of ion insertion and electron transfer. It is worth mentioning that the two-dimensional cluster-based Ni/Co-organic layer (Ni0.7Co0.3-CMOL) inherits high stability from the Kagóme lattice and shows excellent pseudocapacitance behavior. As an optimized atomic composition, this crystalline CMOL exhibits excellent performance and stability both in 1.0 M KOH and All-Solid-State Flexible Asymmetric Supercapacitor (ASCs). The specific capacitance values are 1211 and 394 F g-1 and the energy density is 54.67 Wh kg-1 at 1 A g-1. Good cycling stability is characterized by its capacitance retention, maintained at 92.4% after 5000 cycles in a three-electrode system and 90% after 2000 cycles at 20 A g-1 for assembled All-Solid-State Flexible ASCs. An in situ XRD technique was used in the three-electrode system, which showed that there was no signal of crystalline substance that affected the cyclic stability of the material while charging and discharging. These superior results prove that Ni0.7Co0.3-CMOL is a promising candidate for supercapacitor applications.