The novel acid–base flow battery technology stores electrical energy using pH and salinity gradients in water and is suitable for different capacities (kWh–MWh scale) because of its scalable technology. Due to the flexibility of this system, it is predicted to provide technical, economic, and environmental benefits for supporting renewable energy integration, such as wind and solar energy, within the electricity generation system. However, its level of acceptance might be affected by additional conditioning factors in terms of policies and maintenance. To elucidate the relevance of the possible barriers to the implementation of the innovative AB-FB system, this work introduces an approach based on the analytic hierarchy process developed at three levels of hierarchy under a sustainability perspective. An exhaustive literature review as well as an assessment of experts’ evaluations were performed to identify the barriers in terms of technical, economic, environmental, policy, and maintenance aspects. Based on the results, the cost parameters (mostly attributed to the stack cost), followed by technical and environmental criteria, were deemed to be of the highest priority.