In this paper, we introduce a self-supervised deep SLAM method that robustly operates in dynamic scenes while accurately identifying dynamic components. Our method leverages a dual-flow representation for static flow and dynamic flow, facilitating effective scene decomposition in dynamic environments. We propose a dynamic update module based on this representation and develop a dense SLAM system that excels in dynamic scenarios. In addition, we design a self-supervised training scheme using DINO as a prior, enabling label-free training. Our method achieves superior accuracy compared to other self-supervised methods. It also matches or even surpasses the performance of existing supervised methods in some cases. All code and data will be made publicly available upon acceptance.