We investigate the spectral properties of the brightest gamma-ray flares of blazars detected by the Fermi Large Area Telescope. We search for the presence of spectral breaks and measure the spectral curvature on typical time scales of a few days. We identify significant spectral breaks in fewer than half of the analyzed flares, but their parameters do not show any discernible regularities, and in particular there is no indication for gamma-ray absorption at any fixed source-frame photon energy. More interestingly, we find that the studied blazars are characterized by significant spectral variability. Gamma-ray flares of short duration are often characterized by strong spectral curvature, with the spectral peak located above 100 MeV. Since these spectral variations are observed despite excellent photon statistics, they must reflect temporal fluctuations in the energy distributions of the emitting particles. We suggest that highly regular gamma-ray spectra of blazars integrated over long time scales emerge from a superposition of many short-lived irregular components with relatively narrow spectra. This would imply that the emitting particles are accelerated in strongly turbulent environments. Show Partial Abstract