Flat spectrum radio quasars (FSRQs) are the most luminous blazars at GeV energies, and may be producers of extremely high energy astrophysical neutrinos. However, at TeV energies, only a few such objects have been observed to emit gamma rays, typically during bright GeV flares. We report on the gamma-ray variability and spectral characteristics of three FSRQs that have been observed at TeV energies by VERITAS: 3C 279, PKS 1222+216, and Ton 599. We use a procedure based on Bayesian blocks to identify gamma-ray flares and model the broadband spectral energy distributions of PKS 1222+216 and Ton 599 during TeV detections by VERITAS during flares in 2014 and 2017 to derive constraints on the properties of the gamma-ray emission in these sources. The GeV flux distributions of the three sources are explained well by a physically-motivated stochastic differential equation recently proposed by Tavecchio, Bonnoli, and Galanti (2020), and we interpret the emission in the context of this model.