Due to the difficulty of obtaining ground-truth data for 4D radar scene flow estimation, previous methods typically rely on either self-supervised losses or cross-modal supervision using 3D LiDAR data, 2D images, and odometry. However, self-supervised approaches often yield suboptimal results due to radar's inherently low-fidelity measurements, while existing cross-modal supervised methods introduce complex multi-task architecture and require costly LiDAR sensors to generate pseudo radar scene flow labels from pretrained 3D tracking models. To overcome these limitations, we propose a task-specific iterative framework for weakly supervised radar scene flow learning, using only images and odometry for auxiliary supervision during training. Specially, we establish two novel instance-aware self-supervised losses by exploiting off-the-shelf 2D tracking and segmentation algorithms to obtain tracked instance masks, which are back-projected into 3D space to provide instance-level semantic guidance; for static regions, we integrate vehicle odometry with radar's intrinsic motion cues to construct a rigid static loss. Extensive experiments on the real-world View-of-Delft (VoD) dataset demonstrate that our method not only surpasses state-of-the-art cross-modal supervised approaches that rely on 3D multi-object tracking on dense LiDAR point clouds but also outperforms existing fully supervised scene flow estimation methods. The code is open-sourced at \href{https://github.com/FuJingyun/IterFlow}{https://github.com/FuJingyun/IterFlow}.