Accurate 3D scene flow estimation is critical for autonomous systems to navigate dynamic environments safely, but creating the necessary large-scale, manually annotated datasets remains a significant bottleneck for developing robust perception models. Current self-supervised methods struggle to match the performance of fully supervised approaches, especially in challenging long-range and adverse weather scenarios, while supervised methods are not scalable due to their reliance on expensive human labeling. We introduce DoGFlow, a novel self-supervised framework that recovers full 3D object motions for LiDAR scene flow estimation without requiring any manual ground truth annotations. This paper presents our cross-modal label transfer approach, where DoGFlow computes motion pseudo-labels in real-time directly from 4D radar Doppler measurements and transfers them to the LiDAR domain using dynamic-aware association and ambiguity-resolved propagation. On the challenging MAN TruckScenes dataset, DoGFlow substantially outperforms existing self-supervised methods and improves label efficiency by enabling LiDAR backbones to achieve over 90% of fully supervised performance with only 10% of the ground truth data. The source code will be made publicly available.