As data centers emerge as the information backbone of an increasingly digital world, the associated service demand has been rising rapidly. The operational nature of the data center brings great flexibility potential for energy systems. However, there remains an open question as to how to capture the flexibility potentials of geographically dispersed data centers and incentivize their flexibility provision for system operation. In this paper, we propose electricity–heat coordinated operation to capture the flexibility potential of data centers, i.e., temporal, spatial and integrated energy flexibility. To better depict the interaction between the system operator and the data centers, the centralized coordinated operation model is decomposed into a bilevel model, and an incentivized profit-sharing mechanism is designed to suitably motivate the flexibility provision of data centers. Case studies based on real-world datasets show that incorporating data centers at the system level can effectively improve operation efficiency and facilitate renewable energy integration. Hopefully, our work can provide novel insights into the coordination of data networks and power grids as well as the flexibility potential activation of data centers.