The proliferation of tobacco-related content on social media platforms poses significant challenges for public health monitoring and intervention. This paper introduces a novel multi-modal deep learning framework named Flow-Attention Adaptive Semantic Hierarchical Fusion (FLAASH) designed to analyze tobacco-related video content comprehensively. FLAASH addresses the complexities of integrating visual and textual information in short-form videos by leveraging a hierarchical fusion mechanism inspired by flow network theory. Our approach incorporates three key innovations, including a flow-attention mechanism that captures nuanced interactions between visual and textual modalities, an adaptive weighting scheme that balances the contribution of different hierarchical levels, and a gating mechanism that selectively emphasizes relevant features. This multi-faceted approach enables FLAASH to effectively process and analyze diverse tobacco-related content, from product showcases to usage scenarios. We evaluate FLAASH on the Multimodal Tobacco Content Analysis Dataset (MTCAD), a large-scale collection of tobacco-related videos from popular social media platforms. Our results demonstrate significant improvements over existing methods, outperforming state-of-the-art approaches in classification accuracy, F1 score, and temporal consistency. The proposed method also shows strong generalization capabilities when tested on standard video question-answering datasets, surpassing current models. This work contributes to the intersection of public health and artificial intelligence, offering an effective tool for analyzing tobacco promotion in digital media.