Chronic wounds are a significant burden on individuals and the healthcare system, affecting millions of people and incurring high costs. Wound classification using deep learning techniques is a promising approach for faster diagnosis and treatment initiation. However, lack of high quality data to train the ML models is a major challenge to realize the potential of ML in wound care. In fact, data limitations are the biggest challenge in studies using medical or forensic imaging today. We study data augmentation techniques that can be used to overcome the data scarcity limitations and unlock the potential of deep learning based solutions. In our study we explore a range of data augmentation techniques from geometric transformations of wound images to advanced GANs, to enrich and expand datasets. Using the Keras, Tensorflow, and Pandas libraries, we implemented the data augmentation techniques that can generate realistic wound images. We show that geometric data augmentation can improve classification performance, F1 scores, by up to 11% on top of state-of-the-art models, across several key classes of wounds. Our experiments with GAN based augmentation prove the viability of using DE-GANs to generate wound images with richer variations. Our study and results show that data augmentation is a valuable privacy-preserving tool with huge potential to overcome the data scarcity limitations and we believe it will be part of any real-world ML-based wound care system.