We present high-time-resolution multicolour observations of the quiescent soft X-ray transient V404 Cyg obtained with ULTRACAM. Superimposed on the ellipsoidal modulation of the secondary star are large flares on time-scales of a few hours, as well as several distinct rapid flares on time-scales of tens of minutes. The rapid flares, most of which show further variability and unresolved peaks, cover shorter time-scales than those reported in previous observations. The power density spectrum of the 5-s time-resolution data shows a quasi-periodic oscillation (QPO) feature at 0.78 mHz (=21.5 min). Assuming this periodicity represents the Keplerian period at the transition between the thin and advective disc regions, we determine the transition radius. We discuss the possible origins for the QPO feature in the context of the advection-dominated accretion flow model. We determine the colour of the large flares and find that the i'-band flux per unit frequency interval is larger than that in the g' band. The colour is consistent with optically thin gas with a temperature of ~8000 K arising from a region with an equivalent blackbody radius of at least 2 Rsolar, which covers 3 per cent of the surface of the accretion disc. Our timing and spectral analysis results support the idea that the rapid flares (i.e. the QPO feature) most likely arise from regions near the transition radius.