Due to their high load flexibility and air-quality benefits, axial (sequential) stage combustion systems have become more popular among ground-based power gas turbine combustors. However, inert combustion residuals passing from the initial stage onto the secondary stage affects the reactivity and stability of the flame in the second stage of the combustor. The present study investigates laminar flame characteristics of the combustion within the second stage of a sequential combustor. The method of constant pressure for spherically expanding flames was employed to obtain laminar burning velocities (LBV) and burned gas Markstein lengths (Lb) of premixed methane/air mixtures diluted using flue gas at 3 bar and 423 K. Combustion residuals were imitated using a 19.01% H2O + 9.50% CO2 + 71.49% N2 mixture by volume, while tested dilution ratios were 0%, 5%, 10%, and 15%. Experimental results showed that the LBV was decreased by 18–23%, 36–42%, and 50–52% with additions of 5%, 10%, and 15% combustion products, respectively. As the dilution and equivalence ratios increased, the Lb values increased slightly, suggesting that the stability and stretch of the CH4/air flames increased at these conditions. Numerical results were obtained from CHEMKIN using the GRI-Mech 3.0, USC Mech II, San Diego, HP-Mech, NUI Galway, and AramcoMech 1.3 mechanisms. The GRI-Mech 3.0 and HP-Mech performed best, with an average of 2% and 3% difference between numerical and experimental LBVs, respectively. The thermal-diffusion (TD), dilution (D), and the chemical (C) effects of inert post-combustion gases on the LBV were found using numerical results. The dilution effect was primarily responsible, accounting for 79–84% of the LBV reduction.