As the penetration of intermittent renewable energy increases in bulk power systems, flexible generation resources, such as quick-start gas units, become important tools for system operators to address the power imbalance problem. To better capture their flexibility, we proposed a distributionally robust unit commitment framework with both regular and flexible generation resources, in which the unit commitment decisions for flexible generation resources can be adjusted in the second stage to accommodate the renewable energy intermittency. In order to tackle this two-stage distributionally robust mixed-binary model, to which traditional separation algorithms wont apply, we designed an integer L-shaped algorithm with advanced cutting plane techniques. In comparison to the traditional distributionally robust unit commitment, the proposed approach can reduce the system cost through an improved flexible resource quantification in the modeling.