We examine four electron-dominated flares, two from the GRS instrument on 1989 March 6, and two from the EGRET and BATSE instruments on 1991 June 30 and 1991 July 2. Their photon spectra, which are almost all caused by electron bremsstrahlung radiation, show significant deviations from a simple power-law form. These are attributed to the deviations in the spectra of the accelerated electrons. We develop three stochastic acceleration models to explain the shape of the photon spectra: the hard sphere model, the whistler wave model, and a more general, but still simplified, stochastic acceleration model. For photon emissions, we use a simple sum of the thin target emission from the trapped electrons at the acceleration site near the loop top and the thick target emission from the escaping electrons which travel along the magnetic field lines and radiate in the denser chromosphere at the footpoints. We find that the hard sphere model does not fit any of the flares and can be ruled out. The other two models show that the high-energy cutoff in the two GRS flares can be attributed to synchrotron radiation losses in the presence of a 500 G magnetic field at the acceleration site. The observed break in the photon spectra of all four flares around 1 MeV is attributed to a combination of the energy dependence of the escape time of particles out of the acceleration region and the change in the energy dependence of the bremsstrahlung cross section between the nonrelativistic and relativistic regimes. Further steepening of the spectrum at even lower energies is caused by Coulomb losses at the acceleration site. We find that acceleration timescales as low as ~1 s are possible with a ratio of turbulent to the magnetic field energy densities of ~10-4. We also set limits on the plasma density, the size of the acceleration region, and the spectrum of the plasma turbulence.