The objective of this work is to investigate the aerodynamics and thermal interactions between a spreading flame and the surrounding walls as well as their effects on fire behaviors. A three-dimensional transient Computational Fluid Dynamics combustion model is used to simulate concurrent-flow flame spread over a thin solid sample in a narrow flow duct. The height of the flow duct is the main parameter. The numerical results predict a quenching height for the flow duct below which the flame fails to spread. For duct heights sufficiently larger than the quenching height, the flame reaches a steady spreading state before the sample is fully consumed. The flame spread rate and the pyrolysis length at steady state first increase and then decrease when the flow duct height decreases. The detailed gas and solid profiles show that flow confinement has multiple effects on the flame spread process. On one hand, it accelerates flow during thermal expansion from combustion, intensifying the flame. On the other hand, increasing flow confinement reduces the oxygen supply to the flame and increases conductive heat loss to the walls, both of which weaken the flame. These competing effects result in the aforementioned non-monotonic trend of flame spread rate as duct height varies. Near the quenching duct height, the transient model reveals that the flame exhibits oscillation in length, flame temperature, and flame structure. This phenomenon is suspected to be due to thermo-diffusive instability.