Dynamic magnetic resonance imaging has emerged as a powerful modality for investigating upper-airway function during speech production. Analyzing the changes in the vocal tract airspace, including the position of soft-tissue articulators (e.g., the tongue and velum), enhances our understanding of speech production. The advent of various fast speech MRI protocols based on sparse sampling and constrained reconstruction has led to the creation of dynamic speech MRI datasets on the order of 80-100 image frames/second. In this paper, we propose a stacked transfer learning U-NET model to segment the deforming vocal tract in 2D mid-sagittal slices of dynamic speech MRI. Our approach leverages (a) low- and mid-level features and (b) high-level features. The low- and mid-level features are derived from models pre-trained on labeled open-source brain tumor MR and lung CT datasets, and an in-house airway labeled dataset. The high-level features are derived from labeled protocol-specific MR images. The applicability of our approach to segmenting dynamic datasets is demonstrated in data acquired from three fast speech MRI protocols: Protocol 1: 3 T-based radial acquisition scheme coupled with a non-linear temporal regularizer, where speakers were producing French speech tokens; Protocol 2: 1.5 T-based uniform density spiral acquisition scheme coupled with a temporal finite difference (FD) sparsity regularization, where speakers were producing fluent speech tokens in English, and Protocol 3: 3 T-based variable density spiral acquisition scheme coupled with manifold regularization, where speakers were producing various speech tokens from the International Phonetic Alphabetic (IPA). Segments from our approach were compared to those from an expert human user (a vocologist), and the conventional U-NET model without transfer learning. Segmentations from a second expert human user (a radiologist) were used as ground truth. Evaluations were performed using the quantitative DICE similarity metric, the Hausdorff distance metric, and segmentation count metric. This approach was successfully adapted to different speech MRI protocols with only a handful of protocol-specific images (e.g., of the order of 20 images), and provided accurate segmentations similar to those of an expert human.