Energy flexibility management can significantly support the smoother and more cost-effective green transformation of the energy mix. However, effective management of the flexibility of residential loads can only be achieved if users are successfully engaged into the process. In this paper, we propose an optimization framework that incorporates provision of different forms of monetary and non-monetary incentives to prosumers, i.e., rewards, lotteries, peer-pressure, for providing flexibility at specific time slots. Economic rewards are offered according to a simple, yet very powerful, linear incentives' function. Dynamic tariffs per time slot for purchasing and selling electricity are accommodated in this framework as well. The optimization problem of the DR aggregator is modeled as a cost-minimization one; its solution as a Stackelberg game is outlined for the case of full information on user-utility functions by the DR aggregator. Moreover, a distributed iterative algorithm is developed for solving the flexibility-management problem in the case where user-utility functions are not known to the aggregator. Numerical results show that this optimization framework is able to elicit the required flexibility from users at a minimum incentive cost, especially when monetary rewards are combined with peer pressure.