This paper is devoted to the numerical analysis of the spontaneous acceleration of a slow flame in a semi-closed channel. In particular, the flow development in the channel ahead of the propagating flame is analyzed. The applied detailed numerical model allows the clear observation of all features intrinsic to the reacting flow evolution in the channel, including the formation of perturbations on the scale of the boundary layer and their further development. In all considered cases, perturbations of the boundary layer emerge in the early stages of flame acceleration and decay afterward. The flow stabilizes more rapidly in a narrow channel, where the velocity profile is close to the Poiseuille profile. At the same time, the compression waves generated in the reaction zone travel along the channel. The interaction between compression waves in the area of combustion products can lead to the formation of shock waves. The effect of shock waves on the flow in the fresh mixture causes an increase in the flame area and a corresponding flame acceleration. In addition, shock waves trigger boundary-layer instability in wide channels. The perturbations of the boundary layer grow and evolve into vortexes, while further vortex–flame interaction leads to significant flame acceleration.