Flaky tests are tests that yield different outcomes when run on the same version of a program. This non-deterministic behaviour plagues continuous integration with false signals, wasting developers' time and reducing their trust in test suites. Studies highlighted the importance of keeping tests flakiness-free. Recently, the research community has been pushing forward the detection of flaky tests by suggesting many static and dynamic approaches. While promising, those approaches mainly focus on classifying tests as flaky or not and, even when high performances are reported, it remains challenging to understand the cause of flakiness. This part is crucial for researchers and developers that aim to fix it. To help with the comprehension of a given flaky test, we propose FlakyCat, the first approach for classifying flaky tests based on their root cause category. FlakyCat relies on CodeBERT for code representation and leverages a Siamese network-based Few-Shot learning method to train a multi-class classifier with few data. We train and evaluate FlakyCat on a set of 343 flaky tests collected from open-source Java projects. Our evaluation shows that FlakyCat categorises flaky tests accurately, with a weighted F1 score of 70%. Furthermore, we investigate the performance of our approach for each category, revealing that Async waits, Unordered collections and Time-related flaky tests are accurately classified, while Concurrency-related flaky tests are more challenging to predict. Finally, to facilitate the comprehension of FlakyCat's predictions, we present a new technique for CodeBERT-based model interpretability that highlights code statements influencing the categorization.