The EXTraS project, based on data collected with the XMM-Newton observatory, provided us with a vast amount of light curves for X-ray sources. For each light curve, EXTraS also provided us with a set of features (https://extras.inaf.it). We extract from the EXTraS database a tabular dataset of 31832 variable sources by 108 features. Of these, 13851 sources were manually labeled as stellar flares or non-flares based on direct visual inspection. We employed a supervised learning approach to produce a catalog of stellar flares based on our dataset, releasing it to the community. We leverage explainable AI tools and interpretable features to better understand our classifier. We train a gradient boosting classifier on 80% of the data for which labels are available. We compute permutation feature importance scores, visualize feature space using UMAP, and analyze some false positive and false negative data points with the help of Shapley additive explanations - an AI explainability technique used to measure the importance of each feature in determining the classifier's prediction for each instance. On the test set made up of the remainder 20% of our labeled data, we obtain an accuracy of 97.1%, with a precision of 82.4% and a recall of 73.3%. Our classifier outperforms a simple criterion based on fitting the light curve with a flare template and significantly surpasses a gradient-boosted classifier trained only on model-independent features. False positives appear related to flaring light curves that are not associated with a stellar counterpart, while false negatives often correspond to multiple flares or otherwise peculiar or noisy curves. We apply our trained classifier to currently unlabeled sources, releasing the largest catalog of X-ray stellar flares to date. We estimate that integrating our classifier into the astronomers' workflow will reduce the time spent visually inspecting light curves by approximately half compared to an approach based on flare template fitting, with implications for the classification of sources whose variability is less well established within EXTraS as well as for other catalogs and, possibly, forthcoming missions.