Phase-change memory (PCM) is a promising candidate for data storage in flexible electronics, but its high switching current and power are often drawbacks. In this study, we demonstrate a switching current density of ~0.1 mega-ampere per square centimeter in flexible superlattice PCM, a value that is one to two orders of magnitude lower than in conventional PCM on flexible or silicon substrates. This reduced switching current density is enabled by heat confinement in the superlattice material, assisted by current confinement in a pore-type device and the thermally insulating flexible substrate. Our devices also show multilevel operation with low resistance drift. The low switching current and good resistance on/off ratio are retained before, during, and after repeated bending and cycling. These results pave the way to low-power memory for flexible electronics and also provide key insights for PCM optimization on conventional silicon substrates.