Increasing emission concerns about greenhouse gases have led to an increasing tendency to use renewable energy sources (RERs) in the power system. Nevertheless, the probabilistic nature of RERs has led to an enhanced require to flexibility provision. Hence, it is necessary to implement a flexibility-based generation maintenance scheduling. For this purpose, it has used the flexibility index of the system in order to evaluate the flexibility of the power system. In flexibility studies, modeling and predicting the variability of renewable resources is important. In this paper, the uncertainties of wind are considered through forecasting by deep learning method in Python. Gas-fired power plants are one of the most important suppliers of flexibility in the supply-side. Therefore, the reliable operation of power system depends on the of natural gas availability. Furthermore, gas demand is subject to various uncertainties, especially in cold seasons, which will have significant effects on power system. in this paper, power-to-gas (P2G) technology as energy storages is modeled to mitigate the impact of wind output and gas demand uncertainty. Meanwhile, integrated natural gas and electricity demand response such as event-based and time-based model has been applied as a flexibility provision from demand-side point of view. In this paper, the objectives of reducing emission and costs, leveling the reserve margin and increasing flexibility are considered as the objectives of optimizing generation maintenance scheduling. In order to solve the multi-objective problem, the augmented Epsilon constraint method has been used. The proposed model has been implemented on a modified IEEE RTS 24 bus.