Multi-view clustering aims to improve the final performance by taking advantages of complementary and consistent information of all views. In real world, data samples with partially available information are common and the issue regarding the clustering for incomplete multi-view data is inevitably raised. To deal with the partial data with large scales, some fast clustering approaches for incomplete multi-view data have been presented. Despite the significant success, few of these methods pay attention to learning anchors with high quality in a unified framework for incomplete multi-view clustering, while ensuring the scalability for large-scale incomplete datasets. In addition, most existing approaches based on incomplete multi-view clustering ignore to build the relation between anchor graph and similarity matrix in symmetric nonnegative matrix factorization and then directly conduct graph partition based on the anchor graph to reduce the space and time consumption. In this paper, we propose a novel fast incomplete multi-view clustering method for the data with large scales, termed Fast Incomplete Multi-view clustering by flexible anchor Learning (FIML), where graph construction, anchor learning and graph partition are simultaneously integrated into a unified framework for fast incomplete multi-view clustering. To be specific, we learn a shared anchor graph to guarantee the consistency among multiple views and employ a adaptive weight coefficient to balance the impact for each view. The relation between anchor graph and similarity matrix in symmetric nonnegative matrix factorization can also be built, i.e., each entry in the anchor graph can characterize the similarity between the anchor and original data sample. We then adopt an alternative algorithm for solving the formulated problem. Experiments conducted on different datasets confirm the superiority of FIML compared with other clustering methods for incomplete multi-view data.