Automatic fluency assessment (AFA) remains challenging, particularly in capturing speech rhythm, pauses, and disfluencies in non-native speakers. We introduce a chunk-based approach integrating self-supervised learning (SSL) models (Wav2Vec2, HuBERT, and WavLM) selected for their complementary strengths in phonetic, prosodic, and noisy speech modeling, with a hierarchical CNN-BiLSTM framework. Speech is segmented into breath-group chunks using Silero voice activity detection (Silero-VAD), enabling fine-grained temporal analysis while mitigating over-segmentation artifacts. SSL embeddings are fused via a learnable weighted mechanism, balancing acoustic and linguistic features, and enriched with chunk-level fluency markers (e.g., speech rate, pause durations, n-gram repetitions). The CNN-BiLSTM captures local and long-term dependencies across chunks. Evaluated on Avalinguo and Speechocean762, our approach improves F1-score by 2.8 and Pearson correlation by 6.2 points over single SSL baselines on Speechocean762, with gains of 4.2 F1-score and 4.0 Pearson points on Avalinguo, surpassing Pyannote.audio-based segmentation baselines. These findings highlight chunk-based multi-SSL fusion for robust fluency evaluation, though future work should explore generalization to dialects with irregular prosody.