This study proposes a modeling approach to simulate the thermo-chemo-mechanical responses of thermal barrier coatings (TBCs) exposed to flowing high-temperature gas. A thermal-fluid-solid analysis was performed to simulate temperature fields of the coatings under flowing gas environment, while finite element analysis was carried out to study the oxidation and stress evolutions of the coatings using a developed chemo-mechanical constitutive model. Thermal loads from thermal-fluid-solid analysis were imposed on the finite element model, by which the factors associated with flowing gas were incorporated into the thermo-chemo-mechanical modeling. The study systematically investigated the effects of flowing gas and coolant on the chemo-mechanical responses of the coatings. The results revealed that the enhanced gas factors (temperature, velocity, angle of attack, and pressure) and coolant temperatures accelerate oxidation and induce higher residual stresses, while higher coolant velocity mitigates both oxidation and stresses. The volume fraction of oxygen in the gas was found to have a negligible influence. Dimensional analysis and multiple regression were performed to derive mathematical expressions for assessing out-of-plane stress and oxidation dynamics. Design maps were proposed to guide the durable design of the coatings.