Demand flexibility management, often by means of Demand Response (DR), can significantly enhance the stability of the electric grid and reduce the investment cost for infrastructure upgrades in case of dynamic energy mix with renewable sources. However, uncertainty in the consumer response to the DR signals may disrupt this goal. In this paper, we deal with the optimal management of the flexibility offered by residential users under uncertainty. We develop a probabilistic user model to account for the uncertainty in the actual provision of the flexibility by a user in conjunction with incentives' offered thereto, which we subsequently introduce in the Demand Response (DR) targeting process. We consider a suitable optimization framework to enable flexibility maximization and budget minimization as separate single-objective expressions with the appropriate constraints. We define representative problems and solve them numerically for a wide range of user parameters, in order to illustrate the applicability and accuracy of our method, and to extract valuable insights. Finally, we develop techniques to resolve practical issues and to enable real-world implementation of the proposed scheme in pilot sites; namely, a mathematical expression to estimate the confidence intervals of the attained flexibility and a learning algorithm for extracting the individual user parameters according to their participation patterns.