Urban road systems often suffer from congestion, which reduces traffic efficiency and increases delays. Traditional flow-based algorithms, such as Edmonds-Karp, respect network capacity but ignore dynamic congestion, whereas shortest path heuristics optimise distance or time but overlook flow constraints. This study proposes a hybrid routing model that combines Edmonds-Karp maximum flow, dynamic congestion modelling, and congestion-aware shortest path heuristics. Edmonds-Karp ensures capacity limits are respected, while congestion updates and weighted path selection enable adaptive rerouting. Vehicle movement was simulated using linear interpolation (LERP) to visualise congestion and routing decisions. Simulations on a sample city network showed that the hybrid approach reduced congestion buildup and improved travel efficiency compared with conventional methods, making it well-suited for autonomous navigation, intelligent transportation, and smart city traffic management.