Increasing the penetration of renewables in prosumers' side brings about operational challenges in the distribution grid due to their variable and uncertain behavior. In fact, these resources have increased the distribution grid net load fluctuation during recent years. In this paper, the flexibility-oriented stochastic scheduling of a microgrid is suggested to capture the net load variability at the distribution grid level. In this scheduling, the flexibility limits are set to manage the net load fluctuation at a desirable level for the main grid operator. The uncertainties of load and renewables are considered, and their uncertainties are under control by the risk-averse strategy. Moreover, multi-period islanding constraints are added to the problem, preparing the microgrid for a resilient response to disturbances. The model is examined on a typical distribution feeder consisting of prosumers and a microgrid. The numerical results are compared for both flexibility-oriented and traditional scheduling of a microgrid in the distribution level. The proposed model reduces the net load ramping of the distribution grid using an efficient dispatch of resources in the microgrid. A sensitivity analysis is also carried out to show the effectiveness of the model.