This paper presents a novel two-stage hierarchical energy management framework based on Model Predictive Control for Local Energy Communities equipped with a Community Energy Storage system. The first stage involves decentralized cost-minimization by individual Building Energy Management Systems for each building, considering real-time electricity prices and user preferences. The second stage, performed by the Community Energy Management System, coordinates the optimized power profiles from BEMSs to maximize the LEC's self-sufficiency and self-consumption, thereby enhancing sustainability. The framework also enables real-time provision of flexibility services, including load flexibility and CES capacity sharing, to the grid aggregator. Flexibility is quantified using an envelope-based approach, and a novel cost structure ensures that the aggregator compensates for any increased operational costs. Simulations on a three-building LEC (residential, office, healthcare) over weekly to yearly periods demonstrate that the hierarchical approach maintains near-optimal performance (average objective degradation of only 1.37% compared to a centralized benchmark) while significantly reducing computation time, which remains independent of the number of buildings. Yearly self-sufficiency and self-consumption reach 0.54 and 0.46, respectively. This work provides the first investigation of CES provision of ancillary services with fair profit allocation, offering a scalable and privacy-preserving solution for practical LEC deployment.