In several applications concerning underground flow simulations in fractured media, the fractured rock matrix is modeled by means of the Discrete Fracture Network (DFN) model. The fractures are typically described through stochastic parameters sampled from known distributions. In this framework, a very large number of simulations may be needed for performing uncertainty quantification (UQ) analyses and it is worth considering the application of suitable complexity reduction techniques. Herein, we propose the application of Neural Networks to flux regression problems in a DFN characterized by stochastic trasmissivities, as an approach to predict fluxes and, as such, speeding up UQ computations.