To investigate the application of hybrid technology in scenarios with high concern for system self-accommodation rapidity, an operationally flexible configuration based on SOFC and twin-shaft free turbine engine has been proposed in this research. The corresponding turbomachinery matching expressions are integrated with thermodynamic and electrochemical descriptions in the novel model so that mechanical equilibrium running states can be guaranteed throughout design and off-design analysis. Inclusion of SOFC and combustor pressure losses (3% and 5%) in high-pressure turbine design can effectively alleviate poor turbine operation and improve cell voltage by 54%, thermal efficiency by 31% under design conditions. For the hybrid gas generator, an integrated calculation algorithm has been developed to satisfy both flow and work compatibility requirements, which essentially constitute a closed binary nonlinear equation set after allowed assignment. The coupling of SOFC not only affects along stream parameters, but also imposes restrictions on the solution scope of the equation set from both horizontal and vertical directions. The flow compatibility between the two mechanically separated turbines finally enables the depiction of equilibrium running line/point on turbomachinery characteristics. With one of the appropriate pairing designs of turbines, the running line can pass through the point of rated rotational speed and compression ratio, where a thermal efficiency of 49.3% is achieved.