Safety margins of aerospace structures can be improved through altering the laminate parameters of composite materials to increase flutter and divergence velocities. Existing work demonstrates the impact of material uncertainties on low-fidelity structural models that are not sufficient to represent realistic aircraft designs. A gap exists in quantifying laminate parameter uncertainties on aeroelasticity for high-fidelity three-dimensional composite structures in realistic tailored designs. This paper puts forward an efficient methodology for uncertainty quantification on the aeroelastic characteristics of three-dimensional composite structures using FE-based parametric composite models and advanced Kriging surrogate models. The methodology is tested on both low and high fidelity case studies to represent the composite wing structure. Similarities between the case studies are observed in the coefficient of variance of all hard flutter modes being within 0.15-1.4% of each other. The difference was found for divergence and soft flutter velocities where the coefficient of variance could be over ten times higher in the high fidelity case. Global sensitivity results revealed similar physical behavior cases can be produced from both studies at early design stages.