3D single object tracking (SOT) is a crucial task in fields of mobile robotics and autonomous driving. Traditional motion-based approaches achieve target tracking by estimating the relative movement of target between two consecutive frames. However, they usually overlook local motion information of the target and fail to exploit historical frame information effectively. To overcome the above limitations, we propose a point-level flow method with multi-frame information for 3D SOT task, called FlowTrack. Specifically, by estimating the flow for each point in the target, our method could capture the local motion details of target, thereby improving the tracking performance. At the same time, to handle scenes with sparse points, we present a learnable target feature as the bridge to efficiently integrate target information from past frames. Moreover, we design a novel Instance Flow Head to transform dense point-level flow into instance-level motion, effectively aggregating local motion information to obtain global target motion. Finally, our method achieves competitive performance with improvements of 5.9% on the KITTI dataset and 2.9% on NuScenes. The code will be made publicly available soon.