The application of soft open points with energy storage (E-SOP) in flexible interconnected distribution networks (FIDN) poses new challenges for reliability assessment, and the "dual-carbon" goals urgently require electricity-carbon synergistic evaluation. Addressing the complex fault characteristics of E-SOP, difficulties in handling wind-solar uncertainties, and the lack of carbon emission considerations in traditional assessment methods, an electricity-carbon synergistic reliability assessment method for FIDN is proposed based on Kantorovich distance scenario reduction and mixed integer linear programming (MILP). Firstly, the basic structure and mathematical model of E-SOP are elaborated. Secondly, wind-solar uncertainty models are constructed, and Copula function models combined with Kantorovich distance-based scenario reduction methods are introduced for processing. Then, electricity-carbon synergistic objective functions are constructed to establish a MILP reliability assessment model with carbon emission constraints. Finally, experimental analysis is conducted on the BUS6 F4 feeder system. Results demonstrate that the proposed method achieves synergistic optimization of reliability and carbon emissions, with SAIFI reduced by 76.2 % and carbon emission saving factor reaching 6.81 %, providing an effective approach for low-carbon reliable operation of flexible interconnected distribution networks.