Recently, flexible electrodes with biaxial/omnidirectional stretchability have attracted significant attention. However, most existing pliable electrode materials can be only stretched in one direction. In this work, an unexpected isotropic van der Waals (vdW) heterostructure is proposed, based on the assembly of two- dimensional crystals of anisotropic black phosphorene (BP) and transition metal carbide (TiC₂). Using vdW-corrected density functional theory calculations, the BP/TiC₂ vdW heterostructure was predicted to have excellent structural and mechanical stability, superior electrical conductivity, omnidirectional flexibility, and a high Li storage capacity. We have unraveled the physical origin of the excellent stability, as well as the Li adsorption preferences of the lithiated heterostructure, based on a three-step analysis of the stability of the Li-adsorption processes. In addition, the BP/TiC₂ vdW heterostructure can also be applied as the anode material for flexible Na-ion batteries because of its high Na storage capacity and strong Na binding. However, compared with Na adsorption, the capacity is higher, and the adsorption energy is more negative for Li adsorption. Our findings provide valuable insights into the exploration of a rich variety of vdW heterostructures for next-generation flexible energy storage devices.