In the context of a flexible interconnected distribution grid, to address the power-energy balance challenges across multiple time scales associated with the large-scale new energy integration, a capacity optimization and configuration scheme involving the integration of both electric and hydrogen hybrid energy storage has been proposed. Initially, a multi-scenario operational strategy for hybrid energy storage is developed in response to the diverse temporal requirements of the flexible interconnected distribution grid. This strategy yields power tasks for the electric-hydrogen hybrid energy storage system (HESS). Building upon a comprehensive consideration of discharge/charge power constraints and state-of-charge limitations for both electric and hydrogen storage components, an energy management strategy is formulated that takes into account the state of charge of the battery energy storage system. Employing a sequential production simulation approach, with the primary goal of maximizing net profit, a capacity configuration model for electric-hydrogen hybrid energy storage is established to balance power and energy across multiple time scales. Finally, utilizing real-world data from a flexible interconnected distribution grid in Hebei Province, the proposed capacity configuration scheme is computed and analyzed. The case study results demonstrate that this scheme can meet the diverse temporal requirements of the flexible interconnected distribution grid system, consequently enhancing overall system economics.