Building flexible asymmetric supercapacitors (ASCs) with high-capacitance, high energy density and a super long life will contribute to the development of new energy storage devices in the future. Although ASCs possess a higher energy density than symmetric supercapacitors (SCs), however, lifespan is effectively degraded during the long-term cycling process. Herein, we demonstrate a high-performance all-solid-state flexible ASC based on battery-type bimetallic oxide (ZnCo2O4) nano-polyhedra supported on carbon fibre textiles (ZCO@CFT) as the cathode and capacitive-type layer structured Ti3C2Tx-MXene as the anode materials. Before assembling the ASC, both electrodes were systematically investigated in aqueous electrolyte and their performance optimized. The ZCO@CFT cathode exhibits high pseudocapacitive charge storage (∼63.22%) with a specific capacitance of 2643.66 F g−1 at 2 A g−1 and Ti3C2Tx-MXene supported on carbon fibre textile (MXene@CFT) exhibits a high specific capacitance of 474.23 F g−1 at 1.5 A g−1 with remarkable cycling stabilities >95%. Furthermore, the ASCs were fabricated using ZCO@CFT as the cathode and MXene@CFT as the anode, (denoted as ZCO‖MXene-ASC) to check the feasibility of the proposed design. The ZCO‖MXene-ASC shows excellent energy storage properties by achieving a high capacitance of 281.25 F g−1 at 0.5 A g−1, a highly competitive energy density of 99.94 W h kg−1 at an admirable power density of 800 W kg−1 with a good life-time >94% over 5000 cycles and flexibility. According to the best of our knowledge, the achieved energy density of ZCO‖MXene-ASC is very competitive, and the highest among all binary metal oxides, carbonaceous materials, and MXene-based SCs and ASCs to date. Our concept of employing 3D bimetallic-oxides and 2D Ti3C2Tx-MXene could open up a new direction in the development of high-performance flexible energy storage devices.