Few-shot intent detection is a challenging task, particularly in scenarios involving multiple labels and diverse domains. This paper presents a novel prototype learning approach that combines the label synset augmentation and the coarse-to-fine prototype distillation for multi-label few-shot intent detection. To tackle the data scarcity issue and the lack of information for unseen domains, we propose to enhance the representations of utterances with label synset augmentation and refine the prototypes by distilling the coarse domain knowledge from a universal teacher model. To solve the multilingual intent detection in real-world dialogue systems, we fine-tune a cross-lingual teacher model to make our method fast adapt to different languages and re-annotate two non-English task-oriented dialogue datasets CrossWOZ and JMultiWOZ in multi-label form. Experimental results on one English and two non-English datasets demonstrate that our approach significantly outperforms existing methods in terms of accuracy and generalization across different domains.