In the context of the ongoing energy transition towards renewable sources and the decentralization of generation, multi-carrier energy systems emerge as a comprehensive solution that allows the synergic integration of different energy carriers, such as electricity, natural gas, heat, and storage, offering an effective response to the challenges posed by the variability of renewable generation and the fluctuation of energy demand. In addition, the inherent flexibility of these systems facilitates the management of the variability of renewable generation and adaptation to changes in energy demand, thus contributing to the stability and reliability of supply. In this context, the participation of prosumers who contribute their distributed generation and load flexibility through energy aggregators that effectively coordinate energy supply and demand in real-time ensures a constant balance in the energy system stands out. This paper explores the potential for various prosumer groups, facilitated by multi-carrier energy aggregators, to offer flexible services to electric distribution and natural gas grid utilities, given that natural gas is the prosumers' primary fuel for heating and cooking. The model is formulated as a two-level optimization problem. The upper level results in the emulation of the distribution system, while the lower level minimizes the flexible demand of prosumers. The interaction of the two levels is not through the price of electricity but through prosumer demand. The resulting optimization problem is a mixed-integer linear programming formulation. The results on the IEEE 33-bus distribution and 20-bus natural gas systems allow us to observe that the supply costs in the distribution and natural gas networks are efficiently reduced considering the coordination of prosumers' participation.