Through a comprehensive investigation into the stability of the combustion chamber in aircraft engines, this study aims to enhance its operational efficiency and safety under variable and complex conditions. By constructing and validating models for flame stability, acoustic coupling effects, and reaction kinetics, the research delves into the specific impacts of the interactions between the flow field, thermal field, and acoustic field on flame stability within the combustion chamber. The findings indicate that a finely optimized combustion chamber design and control parameters significantly improve flame stability, while also reducing the adverse effects of turbulence and acoustic waves on combustion efficiency. These insights provide valuable theoretical and practical guidance for the design and optimization of aircraft engine combustion chambers.