We develop a new type of heterostructure nanocomposite made of reduced graphene oxide-boron carbon nitride nanosheets (rGO-BCN) by B-C covalent bonds. The rGO-BCN nanocomposite delivers a large specific surface and excellent electrochemical properties, and is then constructed into flexible fabric-based high-performance supercapacitor electrodes based on the microfluidic electrospinning technology.