Conducting flexible carbon fiber (CF) cloth was used as a substrate for the hydrothermal growth of nickel hydroxide (Ni(OH)2) and cobalt hydroxy carbonate [Co(OH)xCO3] with unique hierarchical flowery architecture and then was used as a flexible supercapacitor electrode. In a three-electrode configuration in 6 M KOH aqueous electrolyte, the CF-Ni(OH)2 and CF-Co(OH)xCO3 electrode showed the maximum specific capacitance of 789 F/g and 550 F/g, respectively, at 2A/g current accompanied by outstanding cycle stability by retaining 99.9% and 99.5% specific capacitance over 1500 consecutive charge-discharge cycles at 5 A/g. However, the low cell voltage (0.4 V) restricted the respective specific energy to 4.38 and 3.05 Wh/kg at a specific power of 100 W/kg. To overcome the issue, two solid state flexible asymmetric supercapacitors were fabricated using the CF-Ni(OH)2 and CF-Co(OH)xCO3 as the anode and sonochemically deposited CNT over carbon fiber as the cathode material in PVA-KOH gel electrolyte. The as-fabricated flexible supercapacitors CF-Ni(OH)2//CF-CNT and CF-Co(OH)xCO3//CF-CNT were able to deliver high specific energy of 41.1 and 33.48 Wh/kg, respectively, at high specific power of 1.4 kW/kg accompanied by excellent cycle stability (retaining 98% and 97.6% specific capacitance, respectively, over 3000 charge-discharge cycle at 5 A/g).