We consider the implications of a model for long-duration gamma-ray bursts in which the progenitor is spun up in a close binary by tidal interactions with a massive black-hole companion. We investigate a sample of such binaries produced by a binary population synthesis, and show that the model predicts several common features in the accretion on to the newly formed black hole. In all cases, the accretion rate declines as approximately t(-5/3) until a break at a time of order 10(4) s. The accretion rate declines steeply thereafter. Subsequently, there is flaring activity, with the flare peaking between 10(4) and 10(5) s, the peak time being correlated with the flare energy. We show that these times are set by the semi-major axis of the binary, and hence the process of tidal spin-up; furthermore, they are consistent with flares seen in the X-ray light curves of some long gamma-ray bursts.