Small language models (SLMs) support efficient deployments on resource-constrained edge devices, but their limited capacity compromises inference performance. Retrieval-augmented generation (RAG) is a promising solution to enhance model performance by integrating external databases, without requiring intensive on-device model retraining. However, large-scale public databases and user-specific private contextual documents are typically located on the cloud and the device separately, while existing RAG implementations are primarily centralized. To bridge this gap, we propose DRAGON, a distributed RAG framework to enhance on-device SLMs through both general and personal knowledge without the risk of leaking document privacy. Specifically, DRAGON decomposes multi-document RAG into multiple parallel token generation processes performed independently and locally on the cloud and the device, and employs a newly designed Speculative Aggregation, a dual-side speculative algorithm to avoid frequent output synchronization between the cloud and device. A new scheduling algorithm is further introduced to identify the optimal aggregation side based on real-time network conditions. Evaluations on real-world hardware testbed demonstrate a significant performance improvement of DRAGON-up to 1.9x greater gains over standalone SLM compared to the centralized RAG, substantial reduction in per-token latency, and negligible Time to First Token (TTFT) overhead.