We present FlowSeek, a novel framework for optical flow requiring minimal hardware resources for training. FlowSeek marries the latest advances on the design space of optical flow networks with cutting-edge single-image depth foundation models and classical low-dimensional motion parametrization, implementing a compact, yet accurate architecture. FlowSeek is trained on a single consumer-grade GPU, a hardware budget about 8× lower compared to most recent methods, and still achieves the best cross-dataset generalization on Sintel Final and KITTI with a relative improvement of 10 and 15% over the previous state-of-the-art, as well as on Spring and LayeredFlow datasets representing a solid step towards more responsible hardware use.