With the rapid development of deep learning, passive recognition of underwater acoustic targets (PR-UAT) has achieved significant progress. In real-world scenarios, the recognition task often changes for each overseas mission, increasing the demand for model flexibility. Although recently proposed one-class classification (OCC) methods in computer vision provide a solution to variable tasks, they cannot be directly applied to PR-UAT due to the characteristics of spectrograms. In this paper, we introduce FOCAL-UAT, a novel approach for Flexible One-class Acoustic Representation Learning for Underwater Acoustic Target Recognition. FOCAL-UAT features a specialized one-class representation learning scheme incorporating our proposed Spectrogram Distribution Augmentation (SDA) to generate sufficient negative samples, and an efficient method for assembling OCC models that requires minimal computational resources and training time. We conduct extensive experiments for OCC, demonstrating that our OCC method effectively captures the distribution of the target class. The assembled models have shown encouraging performance, with classification accuracy exceeding the baseline of supervised learning.