Manipulation of thin materials is critical for many everyday tasks and remains a significant challenge for robots. While existing research has made strides in tasks like material smoothing and folding, many studies struggle with common failure modes (crumpled corners/edges, incorrect grasp configurations) that a preliminary step of layer detection could solve. We present a novel method for classifying the number of grasped material layers using a custom gripper equipped with DenseTact 2.0 optical tactile sensors. After grasping, the gripper performs an anthropomorphic rubbing motion while collecting optical flow, 6-axis wrench, and joint state data. Using this data in a transformer-based network achieves a test accuracy of 98.21\% in classifying the number of grasped cloth layers, and 81.25\% accuracy in classifying layers of grasped paper, showing the effectiveness of our dynamic rubbing method. Evaluating different inputs and model architectures highlights the usefulness of tactile sensor information and a transformer model for this task. A comprehensive dataset of 568 labeled trials (368 for cloth and 200 for paper) was collected and made open-source along with this paper. Our project page is available at https://armlabstanford.github.io/dynamic-cloth-detection.