China's natural disaster situation presents a complex and severe scenario, resulting in substantial human and material losses as a result of large-scale emergencies. Recognizing the significance of aviation emergency rescue, the state provides strong support for its development. However, China's current aviation emergency rescue system is still under construction and encounters various challenges; one such challenge is to match the dynamically changing multi-point rescue demands with the limited availability of aircraft dispatch. We propose a dynamic task assignment model and a trainable model framework for aviation emergency rescue based on multi-agent reinforcement learning. Combined with a targeted design, the scheduling matching problem is transformed into a stochastic game process from the rescue location perspective. Subsequently, an optimized strategy model with high robustness can be obtained by solving the training framework. Comparative experiments demonstrate that the proposed model is able to achieve higher assignment benefits by considering the dynamic nature of rescue demands and the limited availability of rescue helicopter crews. Additionally, the model is able to achieve higher task assignment rates and average time satisfaction by assigning tasks in a more efficient and timely manner. The results suggest that the proposed dynamic task assignment model is a promising approach for improving the efficiency of aviation emergency rescue.