Research and development of flexible lithium-ion batteries (LIBs) with high energy density and long cycle life for portable and wearable electronic devices has been a cutting-edge effort in recent years. In this paper, a novel flexible self-standing anode for LIBs is fabricated successfully, in which NiCoP nanowires (NWs) coated with FeCoP nanosheets (NSs) to form core-shell heterostructure arrays are grown on carbon cloth (CC) (designated as NiCoP-NWs@FeCoP-NSs/CC). The obtained NiCoP-NWs@FeCoP-NSs/CC anode integrates the merits of the one-dimensional (1D) NiCoP-NW core and two-dimensional (2D) FeCoP-NS shell and the CC to show a high lithium-ion storage capacity with long-term cycling stability (1172.6 mA h g-1 at 1 A g-1 up to 300 cycles with a capacity retention of 92.6%). The kinetics studies demonstrate that the pseudocapacitive behavior dominates the fast lithium storage of this anode material. For fundamental mechanistic understanding, density functional theory (DFT) analysis is carried out, and manifests that electronic synergy can boost the superior performance of the NiCoP-NWs@FeCoP-NSs/CC anode. The assembled LiFePO4//NiCoP-NWs@FeCoP-NSs/CC full battery gives a discharge capacity of 469.9 mA h g-1 at 0.5 A g-1 after 500 cycles, and even at 2 A g-1, it still can retain 581.5 mA h g-1. Besides, the soft pack full battery can keep the LED lit continuously when it is folded at different angles and maintain brightness for a period of time, highlighting the large application potential of this flexible LIB for wearable electronic devices. This work provides an idea for the design and construction of advanced metal phosphide flexible electrodes for LIBs.