Data-driven machine learning (ML) methods have been verified to be effective in fault feeder detection (FFD) for small current grounded systems. Standard ML solution assumes that the training data is sufficient and static, which becomes infeasible in practice due to insufficient fault data for a single substation and dynamic changes in the statistical characteristics of fault data. Therefore, a novel data-driven method based on incremental and federated learning (FL) is proposed to address FFD under small samples. In this paper, a stochastic configuration network (SCN), a flat and noniterative training framework, is applied as a fault feeder classifier. Due to the concise structure and pseudo-inverse-based parameter training scheme, the SCN-based classifier can be trained and updated quickly. To get rid of the drawback of insufficient fault samples for a single substation, a FL-based solution is proposed to aggregate the fault feeder knowledge learned from other substations while maintaining local data privacy. Moreover, to adapt to the dynamic nature of the data, this paper proposes an incremental SCN (ISCN) to learn new fault features online and without forgetting. To verify the efficiency and advantages of the proposed scheme, experiments on actual county-level grid company data were performed. Results imply that in addition to improving FFD accuracy under small samples, the proposed method can also perform incremental learning to maintain accuracy in dynamic environments.