Point clouds are a widely available and canonical data modality which convey the 3D geometry of a scene. Despite significant progress in classification and segmentation from point clouds, policy learning from such a modality remains challenging, and most prior works in imitation learning focus on learning policies from images or state information. In this paper, we propose a novel framework for learning policies from point clouds for robotic manipulation with tools. We use a novel neural network, ToolFlowNet, which predicts dense per-point flow on the tool that the robot controls, and then uses the flow to derive the transformation that the robot should execute. We apply this framework to imitation learning of challenging deformable object manipulation tasks with continuous movement of tools, including scooping and pouring, and demonstrate significantly improved performance over baselines which do not use flow. We perform 50 physical scooping experiments with ToolFlowNet and attain 82% scooping success. See https://tinyurl.com/toolflownet for supplementary material.