Flexibility objects, objects with flexibilities in time and amount dimensions (e.g., energy or product amount), occur in many scientic and commercial domains. Managing such objects with existing DBMSs is infeasible due to the complexity, data volume, and complex functionality needed, so a new kind of flexibility database is needed. This paper is the first to consider flexibility databases. It formally defines the concept of flexibility objects (flex-objects), and provide a novel and efficient solution for aggregating and disaggregating flex-objects. This is important for a range of applications, including smart grid energy management. The paper considers the grouping of flex-objects, alternatives for computing aggregates, the disaggregation process, their associated requirements, as well as efficient incremental computation. Extensive experiments based on data from a real-world energy domain project show that the proposed solution provides good performance while still satisfying the strict requirements.