This paper presents a techno-economic analysis for the optimal sizing of a Hybrid Energy Storage System (HESS) integrating a Redox Flow Battery (RFB) and a Supercapacitor (SC) for an Electric Vehicle (EV) charging station. The SC is used for shaving noisy peak loads and ensuring grid stability, while the use of RFB is optimized through genetic algorithm-based multi-period optimization considering time-of-use (ToU) pricing and energy arbitrage. The profitability of HESS is analyzed and evaluated, and the results indicate that, with the current capital costs, utilizing HESS for this specific use case may not always be directly profitable. However, if installation costs were to decrease, employing HESS can become economically advantageous. Additionally, the management tool and optimization algorithms developed for HESS can be highly beneficial in a wide range of other scenarios.