To mitigate the hallucination and knowledge deficiency in large language models (LLMs), Knowledge Graph (KG)-based Retrieval-Augmented Generation (RAG) has shown promising potential by utilizing KGs as an external resource to enhance LLM reasoning.However, existing KG-RAG approaches struggle with a trade-off between flexibility and retrieval quality. Modular methods prioritize flexibility by avoiding the use of KG-fine-tuned models during retrieval, leading to fixed retrieval strategies and suboptimal retrieval quality. Conversely, coupled methods embed KG information within models to improve retrieval quality but at the expense of flexibility.In this paper, we propose a novel flexible modular KG-RAG framework, termed FRAG, which synergizes the advantages of both approaches. FRAG estimates the hop range of reasoning paths based solely on the query and classifies it as either simple or complex.To match the complexity of the query, tailored pipelines are applied to ensure efficient and accurate reasoning path retrieval, thus fostering the final reasoning process. By using the query text instead of the KG to infer the structural information of reasoning paths and employing adaptable retrieval strategies, FRAG improves retrieval quality while maintaining flexibility. Moreover, FRAG does not require extra LLM fine-tuning or calls, significantly boosting efficiency and conserving resources. Extensive experiments show that FRAG achieves state-of-the-art performance with high efficiency and low resource consumption. The code for our method is publicly available at https://github.com/gzy02/FRAG.