This paper proposes a vision-conditioned flow matching (FM) framework for beam prediction in millimeter-wave vehicle-to-infrastructure links. Instead of modeling discrete beam-index sequences, the proposed method learns the temporal evolution of normalized beam receive power vectors through a continuous vector field governed by an ordinary differential equation, enabling smooth dynamics and efficient sampling. By imposing FM over beam-state transitions and jointly optimizing beam prediction and flow consistency, the proposed framework provides a unified model for future beam prediction. Experimental results show that the proposed FM-based model significantly improves beam prediction performance over baselines, approaches the performance of large language model-based methods, and reduces predictor-side inference latency by about $6.9\times$ on GPU and $2.8\times10^3\times$ on CPU, respectively.