Renewable hydrogen production through sulfur-iodine (SI) cycle is energy efficient and environmentally friendly. Electrochemical cell (EC) has recently been proposed to carry out the Bunsen reaction in the cycle. Existing studies on the EC are limited only to time-consuming experiments whereas cell performance with respect to flow channel is very few. In this study, numerical study is conducted for determining the impact of flow channel on the EC performance of electrochemical Bunsen reaction. Five different configurations of flow channel are physically modelled. A three dimensional, steady state and laminar flow through EC is simulated by solving the governing equations, and show good agreement with experimental data at low current density. It is found that the flow field, local current and potential of serpentine, straight parallel and spiral tubular flow channels distribute almost uniformly, except the significant vortex regions and high resistance at the square bends of straight parallel channel due to the sudden geometric changes. The flow maldistribution in Z-type and U-type parallel flow channels makes them unsuitable for EC. The straight parallel flow channel is found to be optimal due to its low pressure drop as well as low electric power input, followed by serpentine and spiral tubular patterns. The simulation concerning flow channels design favors improving EC performance and the thermal efficiency of SI cycle.