This study examines the impact of variations in side-blowing airflow velocity on plasma generation, combustion wave propagation mechanisms, and surface damage in fused silica induced by a combined millisecond-nanosecond pulsed laser. The airflow rate and pulse delay are the main experimental variables. The evolution of plasma motion was recorded using ultrafast time-resolved optical shadowing. The experimental results demonstrate that the expansion velocities of the plasma and combustion wave are influenced differently by the side-blowing airflow at different airflow rates (0.2 Ma, 0.4 Ma, and 0.6 Ma). As the flow rate of the side-blow air stream increases, the initial expansion velocities of the plasma and combustion wave gradually decrease, and the side-blow air stream increasingly suppresses the plasma. It is important to note that the target vapor is always formed and ionized into plasma during the combined pulse laser action. Therefore, the side-blown airflow alone cannot completely clear the plasma. Depending on the delay conditions, the pressure of the side-blowing airflow, the influence of inverse Bremsstrahlung radiation absorption and target surface absorption mechanisms can lead to a phenomenon known as the double combustion waves when using a nanosecond pulse laser. Both simulation and experimental results are consistent, indicating the potential for further exploration of fused silica targets in the laser field.