Knowledge graphs (KGs), as a structured form of knowledge representation, have been widely applied in the real world. Recently, few-shot knowledge graph completion (FKGC), which aims to predict missing facts for unseen relations with few-shot associated facts, has attracted increasing attention from practitioners and researchers. However, existing FKGC methods are based on metric learning or meta-learning, which often suffer from the out-of-distribution and overfitting problems. Meanwhile, they are incompetent at estimating uncertainties in predictions, which is critically important as model predictions could be very unreliable in few-shot settings. Furthermore, most of them cannot handle complex relations and ignore path information in KGs, which largely limits their performance. In this paper, we propose a normalizing flow-based neural process for few-shot knowledge graph completion (NP-FKGC). Specifically, we unify normalizing flows and neural processes to model a complex distribution of KG completion functions. This offers a novel way to predict facts for few-shot relations while estimating the uncertainty. Then, we propose a stochastic ManifoldE decoder to incorporate the neural process and handle complex relations in few-shot settings. To further improve performance, we introduce an attentive relation path-based graph neural network to capture path information in KGs. Extensive experiments on three public datasets demonstrate that our method significantly outperforms the existing FKGC methods and achieves state-of-the-art performance. Code is available at https://github.com/RManLuo/NP-FKGC.git.