Energy management in a distribution network with multiple microgrids based on the estimation of economic, operational, and flexibility indicators in microgrids is investigated in this paper. The microgrid has a multi-bus structure, which includes renewable wind, solar, and biomass resources, non-renewable resources, and compressed air storage. The objective function is equal to minimizing the operating cost of microgrids and resources. The constraints of the problem include the optimal power distribution equations of microgrids based on flexibility constraints, the utilization model of renewable/non-renewable resources, and energy storage. This scheme has uncertainties of load, energy price, and renewable phenomena. For their modeling, the point estimation method is used to estimate low computational time and accurately model flexibility. To reach a reliable optimal solution with low standard deviation in the final response, a combination of gray wolf optimization algorithms and optimization based on training and learning is used. Numerical results indicate the ability of the proposed scheme to improve the economic and technical conditions of microgrids. Thus, the optimal energy management of the aforementioned resources and storage devices can improve the economic conditions, energy losses, voltage deviation and portable peak load of microgrids by about 54.6%, 39.4%-3.40%, 35.6%-35.9% and 61.9%-3.64%, respectively. In these conditions, the proposed scheme is able to achieve 100% flexibility for microgrids. The proposed solution algorithm has been able to achieve stable computing conditions, such that it has the most optimal solution in low computational time and has a standard deviation of 0.96% in the final response.