Language-instructed robot manipulation has garnered significant interest due to the potential of learning from collected data. While the challenges in high-level perception and planning are continually addressed along the progress of general large pre-trained models, the low precision of low-level action estimation has emerged as the key limiting factor in manipulation performance. To this end, this paper introduces a novel robot manipulation framework, i.e., ActionSink, to pave the way toward precise action estimations in the field of learning-based robot manipulation. As the name suggests, ActionSink reformulates the actions of robots as action-caused optical flows from videos, called "action flow", in a self-supervised manner, which are then used to be retrieved and integrated to enhance the action estimation. Specifically, ActionSink incorporates two primary modules. The first module is a coarse-to-fine action flow matcher, which continuously refines the accuracy of action flow via iterative retrieval and denoising process. The second module is a dynamic action flow integrator, which employs a working memory pool that dynamically and efficiently manages the historical action flows that should be used to integrate to enhance the current action estimation. In this module, a multi-layer fusion module is proposed to integrate direct estimation and action flows from both the current and the working memory, achieving highly accurate action estimation through a series of estimation-integration processes. Our ActionSink framework outperformed prior SOTA on the LIBERO benchmark by a 7.9\% success rate, and obtained nearly an 8\% accuracy gain on the challenging long-horizon visual task LIBERO-Long.