This article extends the uncertainty quantification analysis introduced in Paper I for molecular dynamics (MD) simulations of concentration driven ionic flow through a silica nanopore. Attention is now focused on characterizing, for a fixed pore diameter of D = 21 Å, the sensitivity of the system to the Lennard-Jones energy parameters, ɛ(Na(+)) and ɛ(Cl(-)), defining the depth of the potential well for the two ions Na(+) and Cl(-), respectively. A forward propagation analysis is applied to map the uncertainty in these parameters to the MD predictions of the ionic fluxes. Polynomial chaos expansions and Bayesian inference are exploited to isolate the effect of the intrinsic noise, stemming from thermal fluctuations of the atoms, and properly quantify the impact of parametric uncertainty on the target MD predictions. A Bayes factor analysis is then used to determine the most suitable regression model to represent the MD noisy data. The study shows that the response surface of the Na(+) conductance can be effectively inferred despite the substantial noise level, whereas the noise partially hides the underlying trend in the Cl(-) conductance data over the studied range. Finally, the dependence of the conductances on the uncertain potential parameters is analyzed in terms of correlations with key bulk transport coefficients, namely, viscosity and collective diffusivities, computed using Green-Kubo time correlations.