Miniaturized laser-initiated pyrotechnic devices have great application prospects in aerospace and modern weapon systems due to their excellent energy output performance and reliability. In order to develop a low-energy insensitive laser detonation technology based on a two-stage charge structure, it is important to deeply analyze the motion law of a titanium flyer plate driven by the deflagration of the first-stage charge (RDX). The effects of the charge mass of RDX, flyer plate mass, and barrel length on the motion law of flyer plates were studied through a numerical simulation method based on the Powder Burn deflagration model. The consistency between the numerical simulation and the experimental results was analyzed using the paired t confidence interval estimation method. The results show that the Powder Burn deflagration model can effectively describe the motion process of the RDX deflagration-driven flyer plate with a 90% confidence level, and its velocity error is ≤6.7%. The speed of the flyer plate is proportional to the mass of the RDX charge, inversely proportional to the mass of the flyer plate, and exponentially related to its moving distance. As the moving distance of the flyer plate increases, the RDX deflagration products and air in front of the flyer plate are compressed, which inhibits the motion of the flyer plate. In the optimum state (the mass of the RDX charge is 60 mg, the mass of the flyer is 85 mg, and the length of the barrel is 3 mm), the speed of the titanium flyer reaches 583 m/s, and the peak pressure of the RDX deflagration reaches 2182 MPa. This work will provide a theoretical basis for the refined design of a new generation of miniaturized high-performance laser-initiated pyrotechnic devices.