Lithium-ion batteries, serving as the cornerstone of electric vehicles, generate significant thermal output during their operation. This underscores the imperative need for the implementation of an appropriate battery thermal management system (BTMS). Extensive attention has been directed towards thermal-induced flexible phase change material (FPCM) within the domain of BTMS. However, it is notable that the predominant choice in contemporary practice for FPCM in BTMS remains paraffin (PA)-based, sourced from petroleum origins. This study utilizes an environmentally friendly bio-based phase change material (PCM), lauric acid (LA), to fabricate FPCM. The FPCM is skillfully crafted through the incorporation of styrene-ethylene-propylene-styrene (SEPS) and expanded graphite (EG) as supporting materials, forming the LA/SEPS/EG composite phase change material (CPCM). The addition of EG increases the thermal conductivity of CPCM by 4.97 times and enhances the leakage resistance. Furthermore, comprehensive assessments were conducted to evaluate the thermal performance, thermally induced flexibility, heat storage, release characteristics, and cyclic stability of the fabricated FPCM. In the battery discharge tests conducted at 2C/3C/4C rates, the battery containing FPCM consistently maintained its maximum temperature below 50 °C, with a minimal temperature difference of <1 °C, showcasing excellent thermal management performance.