Flexible supercapacitors have recently attracted intense interest. However, achieving high energy density via practical materials and synthetic techniques is a major challenge. Here, we develop a hetero-structured material made of black phosphorous that is chemically bridged with carbon nanotubes. Using a microfluidic-spinning technique, the hybrid black phosphorous-carbon nanotubes are further assembled into non-woven fibre fabrics that deliver high performance as supercapacitor electrodes. The flexible supercapacitor exhibits high energy density (96.5 mW h cm-3), large volumetric capacitance (308.7 F cm-3), long cycle stability and durability upon deformation. The key to performance lies in the open two-dimensional structure of the black phosphorous/carbon nanotubes, plentiful channels (pores <1 nm), enhanced conduction, and mechanical stability as well as fast ion transport and ion flooding. Benefiting from this design, high-energy flexible supercapacitors can power various electronics (e.g., light emitting diodes, smart watches and displays). Such designs may guide the development of next-generation wearable electronics.