Recently, vision transformer based multimodal learning methods have been proposed to improve the robustness of face anti-spoofing (FAS) systems. However, multimodal face data collected from the real world is often imperfect due to missing modalities from various imaging sensors. Recently, flexible-modal FAS~\cite{yu2023flexible} has attracted more attention, which aims to develop a unified multimodal FAS model using complete multimodal face data but is insensitive to test-time missing modalities. In this paper, we tackle one main challenge in flexible-modal FAS, i.e., when missing modality occurs either during training or testing in real-world situations. Inspired by the recent success of the prompt learning in language models, we propose \textbf{V}isual \textbf{P}rompt flexible-modal \textbf{FAS} (VP-FAS), which learns the modal-relevant prompts to adapt the frozen pre-trained foundation model to downstream flexible-modal FAS task. Specifically, both vanilla visual prompts and residual contextual prompts are plugged into multimodal transformers to handle general missing-modality cases, while only requiring less than 4\% learnable parameters compared to training the entire model. Furthermore, missing-modality regularization is proposed to force models to learn consistent multimodal feature embeddings when missing partial modalities. Extensive experiments conducted on two multimodal FAS benchmark datasets demonstrate the effectiveness of our VP-FAS framework that improves the performance under various missing-modality cases while alleviating the requirement of heavy model re-training.