The increasing demand for energy storage systems with high energy and power densities requires suitable electrode materials that are inexpensive, stable, and efficient. Using a facile synthesis technique that yields such materials in a short duration is the need of the hour. Herein, we demonstrate a microwave-assisted hydrothermal technique to synthesize cobalt hydroxy carbonate hydrate with diverse shapes. Upon annealing under air at 500 °C for 3 h, cobalt hydroxy carbonate is converted to phase pure Co₃O₄ without a significant change in the original morphology, i.e., urchin-like, flower-like, and nanocubes. The flower-like structure showed the highest specific capacitance and thus was used as the positive electrode for an all-solid-state flexible asymmetric supercapacitor (ASC) device. Among the three different carbon-based materials such as graphene hydrogel (GH), reduced graphene oxide, and activated carbon tested for use as negative electrodes, GH showed the best performance. The fabricated flexible Co₃O₄//GH ASC device affords an energy density of 29 W h kg⁻¹ at a power density of 916 W kg⁻¹ with a coulombic efficiency of ∼97%. The device retains 87% of its initial capacitance after 2000 cyclic runs.