Robot manipulation critically depends on perception that preserves the action-relevant aspects of a scene. Yet most robot learning pipelines are built upon visual encoders pre-trained for static recognition or vision-language alignment, leaving motion understanding to downstream policies. We introduce DynaFLIP, a dynamics-aware multimodal pre-training framework that pushes motion understanding upstream into perception. We construct image-language-3D flow triplets from heterogeneous human and robot videos, and use these triplets as training-time supervision to shape an image-only encoder. Our key idea is to encourage the three modalities to span a small simplex volume in the shared hyperspherical space -- a smaller simplex volume indicating stronger alignment. To avoid the geometric ambiguity and trivial collapse of naive volume minimization, we combine simplex-volume minimization with a cosine regularizer and a contrastive objective. Our analyses show that DynaFLIP focuses on control-relevant regions critical for manipulation. The resulting dynamics-aware representations serve as reusable visual backbones and consistently outperform baselines across diverse downstream policies, including VLAs. We validate this across diverse simulation and real-world setups, with gains reaching +22.5% under out-of-distribution scenarios. Our results suggest that robot generalization improves when visual representations are trained to encode not just what is present, but how the world changes under action.