Multi-energy integrations provide great opportunities for economic and efficient resource utilization. In the meantime, power system operation requires enough flexible resources to deal with contingencies such as transmission line tripping. Besides economic benefits, this paper focuses on the security benefits that can be provided by multi-energy integrations. This paper first proposes an operation scheme to coordinate multiple energy production and local system consumption considering transmission networks. The integrated flexibility model, constructed by the feasible region of integrated demand response (IDR), is then formulated to aggregate and describe local flexibility. Combined with system security constraints, a multi-energy system operation model is formulated to schedule multiple energy production, transmission, and consumption. The effects of local system flexibility on alleviating power flow violations during N-1 line tripping contingencies are then analyzed through a multi-energy system case. The results show that local system flexibility can not only reduce the system operation costs, but also reduce the probability of power flow congestion or violations by approximately 68.8% during N-1 line tripping contingencies.