Heart sound analysis plays a key role in the early screening and auxiliary diagnosis of cardiovascular diseases. However, conventional auscultation largely depends on physicians' personal experience, which often leads to subjective and inconsistent evaluations. To overcome these limitations, this paper presents an intelligent heart sound classification framework that integrates dynamic mel-frequency cepstral coefficient (MFCC) features with dynamic MFCC-based images. In this work, the static MFCCs together with their first- and second-order derivatives are extracted to describe both the spectral and temporal behaviors of heart sounds. A multi-branch fusion model is designed to enhance feature interaction among the dynamic MFCC features via cross-branch attention. Meanwhile, a CA-ResNet18 network incorporating a coordinate attention mechanism is employed to learn spatio–temporal representations from the dynamic MFCC images. The high-level features produced by both models are then concatenated and classified using a support vector machine. Experimental validation on the PhysioNet Challenge 2016 dataset demonstrates that the proposed method achieves 96.82% accuracy, 97.51% sensitivity, and 96.19% specificity. Comparative studies with recent state-of-the-art methods confirm that the proposed integration of dynamic feature fusion and hybrid deep-learning–machine-learning framework significantly enhances the robustness and classification performance in intelligent heart sound analysis.