This thesis explores the dynamics of hydrogen-enriched methane flames in a swirl-stabilized combustor with axial air injection, a configuration crucial for advancing low-emission combustion technologies. The study focuses on enhancing the understanding of flame behaviour under varying hydrogen enrichment levels, with particular attention to the effects of heat loss and strain on flame shape, mixing, and emissions. Utilizing computational methods, the research investigates key operating scenarios from the APPU project, refining thermal boundary predictions through an improved Heat Resistance Tuning approach. Additionally, it assesses the performance of a necessary flashback-prevention method, Axial Air Injection, quantifying its impact on mixing and flame shape, including their effects on temperature and pollutant formation, with varying results based on the level of hydrogen enrichment in the fuel. The results offer valuable insights that could inform control strategies for the stable and efficient operation of hydrogen-enriched combustion systems, supporting the development of fuel-flexible and environmentally sustainable propulsion technologies.