With the increasing penetration of renewable energy, the volatility and uncertainty of power systems are growing. To achieve flexibility optimization scheduling under expected cost framework while accounting for uncertainties, this paper proposes a multi-regional source-storage-load flexible optimal operation strategy based on information gap decision theory (IGDT). First, for the application scenario of multiple pumped hydro storage (PHS) stations in the East China Grid providing multi-regional supply flexibility, a refined joint scheduling model of multiple PHS stations is established. Next, a source-storage-load flexibility optimization scheduling model that considers resource characteristics is developed, and the output of this deterministic model serves as the baseline cost for the IGDT strategy. Then, by incorporating load and renewable energy uncertainties, a robust model and a risk model are proposed, thereby forming an IGDT-based flexibility optimization scheduling model. Finally, case studies demonstrate that the proposed strategy achieves flexibility optimization scheduling of multi-regional power grids under expected costs while accounting for uncertainties. Moreover, it quantifies the tolerance range of grid uncertainty and flexibility under expected costs, as well as the impacts of uncertain factors on flexible scheduling.