Flexible supercapacitors are important energy storage devices used for wearable and smart electronics. The key to fabricating flexible supercapacitors lies in the acquirement of flexible electrodes. However, design and fabrication of flexible electrodes with both high energy and power densities as well as long cycling life is still a challenge work. Herein, a novel flexible supercapacitor electrode composed of hierarchical FeCo2O4@NiCo-LDH core/shell heterostructures on carbon cloth is reported by a facile and cost-effective method. The electrode exhibits a remarkable specific capacitance of 2426 F g(-1) at 1 A g(-1), and ultrahigh rate capability with 72.5% capacitance retention at 20 A g(-1), as well as excellent cycling stability with a capacitance retention of 91.6% after 5000 cycles. Furthermore, the FeCo2O4@NiCo-LDH/CC as the positive electrode, active carbon as the negative electrode, and PVA-KOH gel as both the solid state electrolyte and separator were assembled into flexible all-solid-state asymmetric supercapacitor. The resulting FeCo2O4@NiCo-LDH//AC ASC device exhibits a maximum energy density of 94.9 Wh kg(-1), and a favorable energy density of 66.5 Wh kg(-1) is still achieved at a high power density of 1.6 kW kg(-1), as well as excellent cycling stability of 88.2% after 5000 cycles. Moreover, the ASC device exhibits outstanding flexible and reliability with no degradation under large twisting, which can light one red LED indicators efficiently. The work presented herein hold promise in energy storage for future portable and wearable electronic devices.