This article introduces and analyzes an integrated energy system that may generate electricity and potable water at a low cost, speeding up the desired clean transition process. The proposed system uses flame-assisted fuel cells to improve upon the inefficiencies of traditional power generation setups by increasing fuel utilization and reducing waste heat. The product's energy cost and overall efficiency are improved by using fuel gas condensation combined with a multi-effect desalination process. The engineering equation solver software examines the feasibility of the proposed system using energy, exergy, exergoeconomic, environmental, and sustainability analyses. The parametric analysis also compares the effects of changing key design variables and performance metrics. Then, the genetic algorithm integrated with an artificial neural network model is applied to minimize the power cost while enhancing the exergy efficiency. According to the results, the proposed efficient hybrid system has an affordable energy cost of 0.123 $/kWh and an environmental impact of 524 kg/MWh. The parametric study demonstrates that increasing the current density improves potable water production while reducing the efficiency and increasing the unfavorable power costs. Also, it can be shown that the sustainability indices improve significantly when a lower fuel utilization factor and equivalence ratio are chosen. The results further reveal that the optimization achieves a higher exergy efficiency of 6.2% and a reduced power cost of 0.03 $/kWh than the design condition. The scatter dispersal of key variables indicates that the fuel utilization factor lacks effectiveness, and keeping the current density and fuel temperature close to their upper limits is techno-economically favorable. Due to the significant temperature increase, mixing of the fuel and air, and chemical interactions between the reactants, the irreversibility analysis shows that the mixer and the flame-assisted fuel cell have the greatest destruction rate under the optimal conditions. © 2023.