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Atmospheric winds are a key physical phenomenon impacting natural hazards, energy transport, ocean currents, large-scale circulation, and ecosystem fluxes. Observing winds is a complex process and presents a large gap in NASA's Earth Observation System. Atmospheric motion vectors (AMVs) aim to fill this gap by making numerical estimates of cloud movement between sequences of multi-spectral satellite images, tracking clouds and water vapor. Recent imaging hardware and software advancements have enabled the use of numerical optical flow techniques to produce accurate and dense vector fields outperforming traditional methods. This work presents WindFlow as the first machine learning based system for feature tracking atmospheric motion using optical flow. Due to the lack of large-scale satellite-based observations, we leverage high-resolution numerical simulations from NASA's GEOS-5 Nature Run to perform supervised learning and transfer to satellite images. We demonstrate that our approach using deep learning based optical flow scales to ultra-high-resolution images of size 2881x5760 with less than 1 m/s bias and 2.5 m/s average error. Four network and learning architectures are compared and it is found that recurrent all-pairs field transforms (RAFT) produces the lowest errors on all metrics for wind speed and direction. Results on held out numerical outputs show RAFT's good performance in each of the spatial, temporal, and physical dimensions. A comparison between WindFlow and an operational AMV product against rawinsonde observations shows that RAFT transfers across simulations and thermal infrared satellite observations. This work shows that machine learning based optical flow is an efficient approach to generating robust feature tracking for AMVs consistently over large regions.