Both pedestrian and robot comfort are of the highest priority whenever a robot is placed in an environment containing human beings. In the case of pedestrian-unaware mobile robots this desire for safety leads to the freezing robot problem, where a robot confronted with a large dynamic group of obstacles (such as a crowd of pedestrians) would determine all forward navigation unsafe causing the robot to stop in place. In order to navigate in a socially compliant manner while avoiding the freezing robot problem we are interested in understanding the flow of pedestrians in crowded scenarios. By treating the pedestrians in the crowd as particles moved along by the crowd itself we can model the system as a time dependent flow field. From this flow field we can extract different flow segments that reflect the motion patterns emerging from the crowd. These motion patterns can then be accounted for during the control and navigation of a mobile robot allowing it to move safely within the flow of the crowd to reach a desired location within or beyond the flow. We combine flow-field extraction with a discrete heuristic search to create Flow-Informed path planning (FIPP). We provide empirical results showing that when compared against a trajectory-rollout local path planner, a robot using FIPP was able not only to reach its goal more quickly but also was shown to be more socially compliant than a robot using traditional techniques both in simulation and on real robots.