Developing an effective safety emergency plan for coal mines is crucial to prevent and reduce accidents, as well as improve the emergency response capability. This paper identifies and analyzes potential accident hazards in the Burtai coal mine through a comprehensive and practical investigation of risk factors. Based on a mathematical model of a mine fire disaster relief algorithm, the MATLAB software is used to conduct numerical simulations of the dynamic spreading process of the fire smoke. Several escape routes are determined based on the simulation results, including the main escape route at the working face of coal mining, the main escape route at the working face of tunneling, and the main escape route against the reverse wind in the main inclined shaft, the auxiliary adit, and the main air intake roadway. The results presented in this study can provide guidance for improving fire emergency escape and rescue plans of the Burtai coal mine.