Nowadays, the increasing integration of variable renewable energies (VREs) in power systems have resulted in operational transformations of energy systems. Respectively, the high-amount of integrated VREs could cause severe-ramping in the net-load of energy systems due to abrupt changes in their power production. Accordingly, based on the limited flexibility capacity in transmission systems, severe ramping-up/down (RU/RD) in distribution systems should be addressed by employing local flexible resources (LFRs). Nevertheless, evolution of multi-agent structured distribution systems has limited the direct access of distribution system operators (DSOs) in scheduling of LFRs. Consequently, this paper intends to organize a bonus-based framework for flexibility RU/RD management in multi-agent distribution systems (MADSs). In this approach, each agent independently operates its resources, while DSO strives to efficiently manage the intense RU/RD associated with the MADS's net electricity demand. Respectively, the proposed approach is modeled as a Stackelberg game and the strong duality concept is deployed to construct the one-level optimizing formulation to determine its equilibrium point. Subsequently, the proposed strategy enables the contribution of LFRs in the RU/RD management of energy systems with high-amount of integrated VREs. Finally, the proposed strategy is applied on a 37-bus-test-system to examine its effectiveness in severe RU/RD mitigation in MADSs.