The development of information and communication technologies and the deregulation of power systems have made the flexible demand participation in bidirectional interaction with power grid possible. The flexible demand can be represented as the flexible reserve provider (FRP) to provide operating reserve through load curtailment and shifting for assisting power system operation. However, the chronological characteristics of curtailment and shifting of FRP may impact the reliability of power systems. Moreover, the uncertainties from customers' participation performances, random failures of information and communication system, and different load types may also influence system operation. In this paper, a novel operating reliability evaluation model for power systems with FRP is proposed utilizing reliability network equivalent (RNE) and time-sequential simulation (TSS) techniques. The RNE technique is developed to include the reserve capacities of FRP incorporating both chronological characteristics and uncertainties. Optimal operation dispatch for system contingencies considering co-optimization of generation and FRP deployment amount is formulated over the entire study period. The TSS method is utilized to assess the operating reliability of restructured power systems. The proposed approaches are validated using the modified IEEE RTS.