The flexibility and high tolerance for mechanical deformation of batteries under operation is a critical aspect of flexible energy storage devices. In this paper, a large-area CNT film (CF) is prepared via chemical vapor deposition (CVD) method and then functionalized with hyperbranched polymers (HP) using the thiol-ene click reaction. CuS microflowers are in-situ grown on the flexible CNTs, where HP significantly enhances interfacial compatibility and greatly enhances the combination of CuS nanosheets with CNTs substrate. The modification strategy effectively promotes Mg2+ conversion reaction of CuS and greatly enhances the stability of the flexible electrode. The as-prepared flexible CuS/CF-HP cathode delivers a high magnesium storage capacity of 178 mAh g−1 at 50 mA g−1 and a good rate performance of 94 mAh g−1 at 2 A g−1, with a high Mg2+ diffusion coefficient of about ∼10−12 cm2 s−1 and a capacity retention rate of 79.2% after 200 cycles at 200 mA g−1. Furthermore, a practical flexible thin-film rechargeable Mg battery device based on the CuS/CF-HP cathode and Mg powder/CF anode was fabricated in a sealed polydimethylsiloxane package. The flexible full battery provides an outstanding power output as well as remarkable mechanical durability, demonstrating its potential applications for flexible energy storage devices.