In recent years, boundary layer flame flashback (BLF) has re-emerged as a technological and operational issue due to the more widespread use of alternative fuels as a part of a global effort to promote carbon neutrality. While much understanding has been achieved in experiments and simulations of BLF in the past decades, the theoretical modeling of BLF still largely relies on the progress made as early as the 1940s, when the critical gradient model (CGM) for the laminar flame flashback was proposed by Lewis and von Elbe. The CGM does not account for the modification of the upstream flow by the flame, which has been recently shown to play a role in BLF. The aim of the present work is to gain additional insight into the effects of thermal gas expansion and confinement on the flame-flow interaction in laminar BLF. Two-dimensional simulations of the confined laminar BLF in a channel are performed in this work. The parametric study focuses on the channel width, the thermal gas expansion coefficient, and the heat losses to the wall. This study evaluates the influence of these factors on the critical condition for the flame flashback. By varying the channel width, it is demonstrated that at the critical condition, the incoming flow in narrow channels is modified globally by the thermal gas expansion, while in wider channels, the flow modification by the flame tends to be more local. In narrow channels, a non-monotonic dependence of the critical-condition centerline velocity on the channel width has been identified. The variation of the heat loss to the wall confirms that the wall’s thermal conditions can significantly alter the flashback limit, with the flashback propensity being larger when the thermal resistance of the wall is high. To assess the general applicability of the CGM, the flame consumption speed and the flow velocity near the wall are quantified. The results confirm that the assumption of flame having no influence on the upstream flow, employed in the CGM, is not fulfilled under confinement for a realistic thermal gas expansion. This results in a general disagreement between the simulations and the CGM, which implies that the thermal expansion effects should be accounted for when considering the confined boundary layer flashback limits. It is shown that the critical velocity gradient increases with the gas expansion coefficient for the given channel width and wall thermal condition.