We present the results of high time resolution optical photometry of five quiescent soft X-ray transients (SXTs): V404 Cyg, A0620-00, J0422+32, GS 2000+25, and Cen X-4. We detect fast optical variations superposed on the secondary star's double-humped ellipsoidal modulation. The variability resembles typical flare activity and has amplitudes ranging from 0.06 to 0.6 mag. Flares occur on timescales of minutes to a few hours, with no dependency on orbital phase, and contribute ~19%-46% to the total veiling observed in the R band. We find that the observed level of flaring activity is veiled by the light of the companion star, and therefore, systems with cool companions (e.g., J0422+32) exhibit stronger variability. After correcting for this dilution, we do not find any correlation between the flaring activity and fundamental system parameters. We find no underlying coherent periods in the data, only quasi-periodic variations ranging between 30 and 90 minutes for the short-period SXTs and longer than 1 hr for V404 Cyg. The power-law index of the power spectra is consistent with what is observed at X-rays wavelengths, i.e., a 1/f distribution, which is compatible with the cellular automaton model. Our observed R'-band luminosities, which are in the range 1031-1033 ergs s-1, are too large to be due to chromospheric activity in the rapidly rotating companions. Since the typical timescale of the flares increases with orbital period, they are most likely produced in the accretion disk. The associated dynamical (Keplerian) timescales suggest that flares are produced at ~0.3Rd-0.7Rd. Possible formation mechanisms are magnetic loop reconnection events in the disk or, less likely, optical reprocessing of X-ray flares. In the former scenario, the maximum duration of the flares suggests that the outer disk is responsible for the flare events and so allows us to constrain the sharing timescale to τ~(5-6)Ω-1K.