Many emerging Internet of Things (IoT) applications deployed on cloud platforms have strict latency requirements or deadline constraints, and thus meeting the deadlines is crucial to ensure the quality of service for users and the revenue for service providers in these delay-stringent IoT applications. Efficient flow scheduling in data center networks (DCNs) plays a major role in reducing the execution time of jobs and has garnered significant attention in recent years. However, only few studies have attempted to combine job-level flow scheduling and routing to guarantee meeting the deadlines of multi-stage jobs. In this paper, an efficient heuristic joint flow scheduling and routing (JFSR) scheme is proposed. First, targeting maximizing the number of jobs for which the deadlines have been met, we formulate the joint flow scheduling and routing optimization problem for multiple multi-stage jobs. Second, due to its mathematical intractability, this problem is decomposed into two sub-problems: inter-coflow scheduling and intra-coflow scheduling. In the first sub-problem, coflows from different jobs are scheduled according to their relative remaining times; in the second sub-problem, an iterative coflow scheduling and routing (ICSR) algorithm is designed to alternately optimize the routing path and bandwidth allocation for each scheduled coflow. Finally, simulation results demonstrate that the proposed JFSR scheme can significantly increase the number of jobs for which the deadlines have been met in DCNs.