A major portion of the delay in air traffic management systems (ATMS) in the US arises from stochastic disturbances such as convective weather. However, in current practice, the predicted storm zones are completely avoided as if they are deterministic obstacles. As a result, the current strategy is too conservative and incurs a high delay. In this paper, we seek to reduce the system delay through explicitly modelling the dynamic and stochastic nature of the storms and adding recourse in the routing and flow management problem. We address the multi-aircraft flow management problem using a stochastic dynamic programming algorithm, where the evolution of the weather is modelled as a stationary Markov chain. Our solution provides a dynamic routing strategy for "N-aircraft" that minimizes the expected delay of the overall system while taking into consideration the constraints obtained by the sector capacities, as well as avoidance of conflicts among the aircraft. Our simulation suggests that a significant improvement in delay can be obtained by using our methods over the existing methods.