Deploying multi-robot systems in environments shared with dynamic and uncontrollable agents presents significant challenges, especially for large robot fleets. In such environments, individual robot operations can be delayed due to unforeseen conflicts with uncontrollable agents. While existing research primarily focuses on preserving the completeness of Multi-Agent Path Finding (MAPF) solutions considering delays, there is limited emphasis on utilizing additional environmental information to enhance solution quality in the presence of other dynamic agents. To this end, we propose Flow-Aware Multi-Agent Path Finding (FA-MAPF), a novel framework that integrates learned motion patterns of uncontrollable agents into centralized MAPF algorithms. Our evaluation, conducted on a diverse set of benchmark maps with simulated uncontrollable agents and on a real-world map with recorded human trajectories, demonstrates the effectiveness of FA-MAPF compared to state-of-the-art baselines. The experimental results show that FA-MAPF can consistently reduce conflicts with uncontrollable agents, up to 55%, without compromising task efficiency.