In this paper, we propose a distributionally robust chance constrained (DRCC) optimization problem for the operation of an active distribution network (ADN). The ADN's operator uses the proposed problem to centrally optimize the dispatch plan of his resources, namely photovoltaic (PV) and battery energy storage (BES) systems, and to participate in wholesale real/reactive power and flexibility markets. We model the uncertainties in the problem by knowing a set of probability distributions, i.e., an ambiguity set. The uncertainties include production capability of PV systems, end-users' consumption, requested flexibility by the external network's operator, and voltage magnitude at the point of common coupling (PCC). The resulting formulation is a DRCC optimization problem for which a solution methodology based on freely available solvers is presented. We evaluate the performance of proposed solution in the numerical results section by comparing it with two benchmark models based on stochastic and chance constrained (CC) optimization.