Training Deep Learning classifiers for stroke-based applications requires collecting lots of samples, which is often expensive and time-consuming. Data augmentation (DA) techniques can mitigate this issue by artificially increasing the number of training samples, eventually improving model performance and robustness. Since the effectiveness of DA techniques mostly depends on the task and dataset, researchers have proposed automatic DA methods, mostly for computer vision tasks. Unfortunately stroke-based data remain underexplored. To address this research gap, we propose AutoChainer, an automatic DA technique suitable for stroke-based data, that consists of applying random chains of augmentation transformations. We perform classification tasks on a variety of datasets (including gestures, letters and signatures) and models, showing that AutoChainer achieves state-of-the-art results. It also has the potential to enhance the visual quality of augmented samples, making them more interpretable, and offers easy customization to task-specific requirements, such as balancing classification accuracy and execution time.