Gaussian splatting has recently gained traction as a compelling map representation for SLAM systems, enabling dense and photo-realistic scene modeling. However, its application to monocular SLAM remains challenging due to the lack of reliable geometric cues from monocular input. Without geometric supervision, mapping or tracking could fall in local-minima, resulting in structural degeneracies and inaccuracies. To address this challenge, we propose GaussianFlow SLAM, a monocular 3DGS-SLAM that leverages optical flow as a geometry-aware cue to guide the optimization of both the scene structure and camera poses. By encouraging the projected motion of Gaussians, termed GaussianFlow, to align with the optical flow, our method introduces consistent structural cues to regularize both map reconstruction and pose estimation. Furthermore, we introduce normalized error-based densification and pruning modules to refine inactive and unstable Gaussians, thereby contributing to improved map quality and pose accuracy. Experiments conducted on public datasets demonstrate that our method achieves superior rendering quality and tracking accuracy compared with state-of-the-art algorithms. The source code is available at: https://github.com/url-kaist/gaussianflow-slam.