As the penetration of intermittent renewable energy resources in microgrids (MGs) continues to grow globally, optimal operation management becomes increasingly crucial due to the variability of these sources. One potential solution to this challenge is the use of demand response (DR) programs, which are practical and relatively low-cost options. However, ensuring the security of MG operation also requires evaluating its flexibility by determining the acceptable boundaries of uncertain variables. Additionally, in real-world operational decision-making problems, there is a simultaneous optimization of multiple objectives, including the maximization of system flexibility and the minimization of system cost. This paper presents a methodology for developing a cost-aware flexibility evaluation method for MGs connected to the upstream grid, which are subject to volatile market prices. The model is based on the feasibility analysis of the uncertain space of wind power generation and load, and it also investigates the level of inflexibility present in the system. The impact of the DR program on the flexibility of MGs is quantified through a case study. The case study confirms the success of the proposed method and underscores the significance of cost modeling in flexibility evaluation problems.