Direct numerical simulations (DNS) with detailed chemical kinetics and chemical explosive mode analysis (CEMA) are performed to investigate the effect of operating pressure and hydrogen–methane blending on laminar wrinkled flames at reheat combustion conditions. Building upon previous three-dimensional DNS datasets of reheat hydrogen flames, the present work considers two-dimensional configurations that render computationally-feasible simulations of high-pressure combustion and significantly more complex hydrocarbon chemistry. A geometrically-simplified representation of the reheat combustor is adopted and the thermodynamic states considered in the simulations are carefully chosen to mimic gas turbine operation conditions, which are constrained to achieve a target flame position and flame temperature. The two-dimensional DNS results are first assessed against the available three-dimensional data and then analyzed to extract the main trends exhibited by the reheat combustion process with respect to the fraction of the fuel consumed by spontaneous ignition and flame propagation, for increasing pressures and hydrogen fractions. Due to significant differences in the characteristic features of the velocity and thermal boundary layers between the three-dimensional and the two-dimensional configurations, a different global flame shape is observed (V-shaped flame vs W-shape flame) together with a∼ 10% bias in the fraction of fuel consumed by spontaneous ignition. Crucially, results from the scaling studies reveal very clear trends with a significant decrease in the fuel consumption by spontaneous ignition for increasing pressures and hydrogen fractions, at the conditions investigated. Finally, this study highlights the important role that first-principle direct numerical simulations, even when conducted in computationally affordable two-dimensional simplified geometrical configurations, can play in obtaining detailed insights and quantitative trends useful for the characterization of complex reactive flows. Novelty and significance The reheat burners of the two-stage sequential gas turbine combustors are designed to stabilize flames primarily due to spontaneous ignition. However, prior numerical simulations revealed the presence of an additional assisted-ignition mode aided by recirculation zones. In this study, we used practically feasible two-dimensional direct numerical simulations of premixed hydrogen–air mixtures under lean conditions to quantify the roles of the two flame stabilization modes at different operating pressures. Achieving fundamental understanding of the effect of pressure and hydrogen fraction on flame stabilization is crucial to the development of two-stage sequential combustion and the present two-dimensional calculations provide important new insights. We show that at high pressures, both modes consume fuel to a similar extent. We also investigated the effect of methane blending on flame stabilization. This study also discusses how two-dimensional direct numerical simulations can be leveraged in the design optimization of reheat burners at low technology readiness levels.