Generating consecutive images of lip movements that align with a given speech in audio-driven lip synthesis is a challenging task. While previous studies have made strides in synchronization and visual quality, lip intelligibility and video fluency remain persistent challenges. This work proposes FluentLip, a two-stage approach for audio-driven lip synthesis, incorporating three featured strategies. To improve lip synchronization and intelligibility, we integrate a phoneme extractor and encoder to generate a fusion of audio and phoneme information for multimodal learning. Additionally, we employ optical flow consistency loss to ensure natural transitions between image frames. Furthermore, we incorporate a diffusion chain during the training of Generative Adversarial Networks (GANs) to improve both stability and efficiency. We evaluate our proposed FluentLip through extensive experiments, comparing it with five state-of-the-art (SOTA) approaches across five metrics, including a proposed metric called Phoneme Error Rate (PER) that evaluates lip pose intelligibility and video fluency. The experimental results demonstrate that our FluentLip approach is highly competitive, achieving significant improvements in smoothness and naturalness. In particular, it outperforms these SOTA approaches by approximately $\textbf{16.3%}$ in Fréchet Inception Distance (FID) and $\textbf{35.2%}$ in PER.