Federated Learning (FL) succeeds in collaborative and privacy-preserving ML model training among multiple distributed data owners. To maintain a healthy FL ecosystem, it is crucial to estimate the contributions of all participants fairly. Due to provable fairness, Shapley value (SV) is widely used for contribution estimation in FL. However, current studies focus on static scenarios with fixed participants and neglect the dynamic settings with the random joining or leaving of participants in practice. This paper fills the gap by proposing FedDSV, a novel contribution estimation framework for FL with dynamic participation. FedDSV supports flexible weighting mechanisms and is compatible with the SV fairness properties in dynamic scenarios. To reduce the computational complexity, we propose a Monte Carlo variant sampling method (SMC), which can adapt well to dynamic scenarios and approximate the true SVs. To evaluate the effectiveness and efficiency of our proposed approaches, extensive experiments under different settings (e.g., frequency switching, low-quality detection, etc.) are conducted on both i.i.d and non-i.i.d. distributions. Experimental results demonstrate that FedDSV can reflect the real utility contribution of data sources for dynamic FL, and SMC can approximate the exact dynamic SVs with larger similarities in a much shorter time than the state-of-the-art methods.