Flexible sealing layer of compressed air energy storage (CAES) caverns is prone to crack-induced extrusion failure under high internal pressure. To address this engineering challenge, a novel composite flexible sealing layer, combining butyl rubber with carbon fiber-reinforced polymer (CFRP) is proposed. By introducing CFRP between the sealing layer and the concrete lining, this structure forms a synergistic working system of “flexible sealing and high-strength confinement”. Pressurization simulations of the CAES cavern equipped with the composite flexible sealing layer were conducted based on laboratory test results and a real-world engineering project. The resistance to crack-induced extrusion failure and the synergistic deformation mechanism of the composite layer under various typical lining crack widths (1 mm, 2 mm, and 3 mm) were systematically investigated. The results indicate the following: (1) The composite structure effectively enhanced the anti-extrusion capacity of the flexible sealing layer; under these crack widths, the maximum bearing pressures were increased by 46.80%, 75.10%, and 72.14%, respectively, compared with the single flexible sealing layer. (2) The synergistic working mechanism of “flexible sealing and high-strength confinement” was revealed: the confinement effect of the CFRP effectively restrained the radial deformation of the rubber, reducing its maximum radial displacement from 3.19 mm to 3.02 mm, representing a decrease of 5.33%. (3) Under high internal pressure conditions, although the CFRP bore a high hoop tensile stress, it did not exceed its ultimate failure limit; moreover, the introduction of this structure did not alter the stress states of the concrete lining and the surrounding rock. The research findings elucidate the structural advantages of the composite flexible sealing layer, providing a novel scheme for the safe design of flexible sealing systems in underground CAES caverns under poor surrounding-rock geological conditions or excessively high internal pressure.