Estimating the direction of ambient fluid flow is a crucial step during chemical plume tracking for flying and swimming animals. How animals accomplish this remains an open area of investigation. Recent calcium imaging with tethered flying Drosophila has shown that flies encode the angular direction of multiple sensory modalities in their central complex: orientation, apparent wind (or airspeed) direction, and direction of. Here we describe a general framework for how these three sensory modalities can be integrated over time to provide a continuous estimate of ambient wind direction. After validating our framework using a flying drone, we use simulations to show that ambient wind direction can be most accurately estimated with trajectories characterized by frequent, large magnitude turns. Furthermore, sensory measurements and estimates of their derivatives must be integrated over a period of time that incorporates at least one of these turns. Finally, we discuss approaches that insects might use to simplify the required computations, and present a list of testable predictions. Together, our results suggest that ambient flow estimation may be an important driver underlying the zigzagging maneuvers characteristic of plume tracking animals' trajectories.