Point cloud registration is a crucial issue in visual computing, aiming to determine the superior alteration for harmonizing two point clouds. This paper introduces a Flatformer-based iterative feedback structure for unmanaged point cloud registration, which capitalizes on recent developments in 3D vision and feedback mechanisms. The proposed method addresses the limitations of traditional and knowledge-centered point cloud alignment techniques through the improvement of the feedback mechanism with the introduction of the Flatformer. Specifically, the introduction of the Flatformer module enhances the extraction of multidimensional features such as geometry, texture, and context, while maintaining robustness to geometric transformations and noise. In addition, the optimization of the feedback transformer improves computational efficiency and feature processing power. The experiments were carried out using the ModelNet40 dataset. Compared to the IFNet and PRNet method, our approach reduced the rotation RMSE by 9.98%, the rotation MAE by 2.83%, the translation RMSE by 8.25%, and the translation MAE by 1.49%, demonstrating a significant improvement in alignment accuracy.