In this paper, the performance of a gas turbine (GT) system coupled with a flameless boiler for steam generation for hydrogen production in a solid oxide steam electrolyzer (SOSE), is evaluated. In this design, the GT exhaust gases are conducted to the flameless boiler in which diluted and preheated exhaust gases are applied as an oxidizer in this process. By using a small amount of fuel in the flameless boiler, the hybrid system is enabled to produce the required steam for the SOSE process. The whole generated electrical power by GT is employed in SOSE and produces hydrogen. The effects of fuel flow rate, turbine inlet temperature (TIT), steam temperature, and electrode characteristics on the hybrid system’s performance are assessed. The results indicate that at the constant electrical power in the GT system, when steam temperature increases, the overall SOSE potential decreases. Consequently, the current of the SOSE enhances, resulting in the enhancement of the overall hydrogen production in high steam temperatures. The presented analysis in this paper can perform more analyses to achieve an insightful understanding of green hydrogen production using hybrid systems.