Label-specific features serve as an effective strategy to learn from multi-label data with tailored features accounting for the distinct discriminative properties of each class label. Existing prototype-based label-specific feature transformation approaches work in a three-stage framework, where prototype acquisition, label-specific feature generation and classification model induction are performed independently. Intuitively, this separate framework is suboptimal due to its decoupling nature. In this paper, we make a first attempt towards a unified framework for prototype-based label-specific feature transformation, where the prototypes and the label-specific features are directly optimized for classification. To instantiate it, we propose modelling the prototypes probabilistically by the normalizing flows, which possess adaptive prototypical complexity to fully capture the underlying properties of each class label and allow for scalable stochastic optimization. Then, a label correlation regularized probabilistic latent metric space is constructed via jointly learning the prototypes and the metric-based label-specific features for classification. Comprehensive experiments on 14 benchmark data sets show that our approach outperforms the state-of-the-art counterparts.