Virtual power plants (VPP) aggregate distributed energy resources (DERs) to enhance system operational flexibility while simultaneously offering considerable potential for low-carbon operation. To characterize the aggregated flexibility of VPP with low-carbon objectives, this paper proposes an adaptive robust optimization (ARO) approach incorporating carbon emission constraints. First, a unified model of multi-type distributed energy resources within the VPP is established, and operating constraints such as power and voltage are integrated to construct a high-dimensional state space representing system operation. Second, based on carbon emission flow theory, a state-space model coupling power flow and carbon emission transfer is developed, enabling simultaneous characterization of energy and carbon emissions. This high-dimensional state space is then mapped to a low-dimensional aggregated power flexibility domain at the substation interface via linear dimension reduction. Further, a two-stage ARO model is formulated with the dual objectives of expanding the aggregated flexibility domain and reducing carbon emissions under the worst-case disturbance scenarios. The model is solved using the column-and-constraint generation (CCG) algorithm. Case study results demonstrate that with carbon emission constraints, the system flexibility domain is reduced from 35.365 MW to 33.916 MW, a decrease of 4.098%, while carbon emissions are reduced from 23.491 t to 17.515 t, a reduction of 25.210%. The proposed method effectively balances operational flexibility and low-carbon requirements, offering a feasible approach for characterizing the aggregated flexibility domain of VPP with carbon constraints.