Multi-view subspace Clustering has recently demonstrated remarkable performance in exploring multiple graph structures. Despite its excellent performance on large-scale multi-view data clustering tasks, the application of those approaches in the real world is still limited. Traditional approaches often use fixed anchor selection strategy, leading to clustering results that heavily depend on pre-processing. Additionally, fixed anchor points fail to ensure cross-view consistency which may result in potential anchor misalignment and then reduce clustering performance. To address these issues, we propose a novel method termed Flexible Multi-view Subspace Clustering with Anchor Structure Alignment (FMVSC-ASA). Essentially, our study contributes to cross-view anchor correspondence by aligning anchor graph with the structure alignment module. Moreover, FMVSC-ASA uses an adaptive approach for anchor learning and then constructs anchor graphs separately for each view. The anchor learning, anchor graph construction and structure alignment are integrated into a unified framework for joint optimization, ensuring the full utilization of cross-view consistency and complementarity. Comprehensive experimental results demonstrate the effectiveness of the proposed FMVSC-ASA.