The development of binder-free flexible electrode materials with high surface area and high electrical conductivity is desirable but remains a serious challenge for pseudocapacitive energy storage. In this work, a universal method is developed for synthesizing porous cobalt chalcogenides flakes uniformly grown on carbon fibers (CF@CoX, X = O, S, Se and Te) by a one-step process of annealing four composites of cotton cloth and leaf-like zeolitic imidazolate frameworks. The as-synthesized CF@CoXs have favorable features, including large surface area, high electrical conductivity, and flexible three-dimensional network architectures, which promote the performance of active materials to a greater extent in their energy-storage applications. Used as flexible electrode materials for pseudocapacitive energy storage, the capacitive performance of CF@CoX is comparable superior. Especially for CF@CoS, it shows a high areal specific capacitance of 3576.0 mF cm−2 at a current density of 5.0 mA cm−2 in a three-electrode configuration. Furthermore, an asymmetric flexible supercapacitor assembled using CF@CoS as a positive electrode and active carbon cloth as a negative electrode exhibits a high areal energy density of 149.4 µWh cm−2 at a power density of 4.3 mW cm−2.