This paper introduces an AC stochastic optimal power flow (SOPF) for the flexibility management of electric vehicle (EV) charging pools in distribution networks under uncertainty. The AC SOPF considers discrete utility functions from charging pools as a compensation mechanism for eventual energy not served to their charging tasks. An application of the AC SOPF is described where a distribution system operator (DSO) requires flexibility to each charging pool in a day-ahead time frame, minimizing the cost for flexibility while guaranteeing technical limits. Flexibility areas are defined for each charging pool and calculated as a function of a risk parameter involving the uncertainty of the solution. Results show that all players can benefit from this approach, i. e., the DSO obtains a risk-aware solution, while charging pools/tasks perceive a reduction in the total energy payment due to flexibility services.