This paper presents RAG-KG-IL, a novel multi-agent hybrid framework designed to enhance the reasoning capabilities of Large Language Models (LLMs) by integrating Retrieval-Augmented Generation (RAG) and Knowledge Graphs (KGs) with an Incremental Learning (IL) approach. Despite recent advancements, LLMs still face significant challenges in reasoning with structured data, handling dynamic knowledge evolution, and mitigating hallucinations, particularly in mission-critical domains. Our proposed RAG-KG-IL framework addresses these limitations by employing a multi-agent architecture that enables continuous knowledge updates, integrates structured knowledge, and incorporates autonomous agents for enhanced explainability and reasoning. The framework utilizes RAG to ensure the generated responses are grounded in verifiable information, while KGs provide structured domain knowledge for improved consistency and depth of understanding. The Incremental Learning approach allows for dynamic updates to the knowledge base without full retraining, significantly reducing computational overhead and improving the model's adaptability. We evaluate the framework using real-world case studies involving health-related queries, comparing it to state-of-the-art models like GPT-4o and a RAG-only baseline. Experimental results demonstrate that our approach significantly reduces hallucination rates and improves answer completeness and reasoning accuracy. The results underscore the potential of combining RAG, KGs, and multi-agent systems to create intelligent, adaptable systems capable of real-time knowledge integration and reasoning in complex domains.