In recent years, there has been a growing acknowledgment of the vital significance of energy flexibilitywithin local energy communities (LECs) as a fundamental strategy to optimize the utilization of adiverse array of available resources. At the district level, where flexibility is indispensable for theefficient operation of controllable assets within centralized substations, energy storage systems (ESSs)emerge as central players in achieving this objective. The primary aims encompass reducing electricitycosts and maximizing the self-consumption of interconnected renewable energy systems (RES) withinLECs, all while ensuring the secure and efficient operation of substation components. This challengeinvolves translating these objectives into a nonlinear optimization problem. Numerous optimizationtechniques have been explored and validated in this pursuit, applied on a real data for the heatingdemand of the ENVIPARK energy district in Turin, Italy. For this regard, a virtual scenario wasconstructed, suggesting the installation of two key energy storage technologies: battery electric storagesystem (BESS) and sensible thermal energy storage (TES). As a long-term assessment, the impact ofenergy flexibility margin, specifically BESS state of charge (SOC) and TES maximum temperature, hasbeen accurately evaluated and quantified. Essentially, adjusting BESS SOC lower limit from 50 % to10 % and the variation interval of the TES maximum temperature from 15 °C to 20 °C led to asubstantial improvement of up to 13.9 % in energy costs. Which underscores the central role of theoptimization-driven energy flexibility in reducing the heating expenses of local energy communities.