Microgrids, storage technologies and renewables are cited as viable options to address resilience challenges faced by the power grids due to natural or man-made disasters. They are also cited as enablers for the recent research interest in low voltage DC microgrids. In this work, an architecture of a resilient small community of microgrids is presented. Furthermore, a distributed and adaptive energy management system is proposed for the tertiary power flow control of a small cluster of DC microgrids, that operate in a cooperative manner to achieve a high level of independence and resilience. To do this, each microgrid accepts to share its storage and generation resources either for economic reasons or for security in case of emergency situations. The proposed EMS replaces the conventional tertiary control that adjusts the power set points of the microgrids' cluster with a cooperative-based power exchange regulator. The model is based on a general-consensus problem and by making use of modern stochastic optimization techniques, such as stochastic-adaptive mixed integer programming. On the physical layer, where the actual commands are sent from the EMS layer to each power flow converter, an exchange of data occurs only with its neighboring converters (adjacent nodes). This is modeled as a sparse communication graph spanned across the microgrids' cluster.