In this article, uncertainty quantification is applied to molecular dynamics (MD) simulations of concentration driven ionic flow through a silica nanopore. We consider a silica pore model connecting two reservoirs containing a solution of sodium (Na(+)) and chloride (Cl(-)) ions in water. An ad hoc concentration control algorithm is developed to simulate a concentration driven counter flow of ions through the pore, with the ionic flux being the main observable extracted from the MD system. We explore the sensitivity of the system to two physical parameters of the pore, namely, the pore diameter and the gating charge. First we conduct a quantitative analysis of the impact of the pore diameter on the ionic flux, and interpret the results in terms of the interplay between size effects and ion mobility. Second, we analyze the effect of gating charge by treating the charge density over the pore surface as an uncertain parameter in a forward propagation study. Polynomial chaos expansions and Bayesian inference are exploited to isolate the effect of intrinsic noise and quantify the impact of parametric uncertainty on the MD predictions. We highlight the challenges arising from the heterogeneous nature of the system, given the several components involved, and from the substantial effect of the intrinsic thermal noise.