We investigate the observational consequences of a binary model for long-duration gamma-ray bursts, in which the star producing the burst is in a close binary with a massive black-hole companion. This allows tidal interactions within the binary to keep the star spun up, which is necessary in order to form the accretion disc that powers the burst. We model the interaction of the supernova ejecta with the black hole companion and find that there are several robustly predicted features in the resulting accretion on to the disc that powers the gamma-ray burst. First, the accretion history shows a break at around 104 s. This is caused by the presence of the Roche lobe truncating the supply of material to the disc. Secondly, the draining of material that has built up in the disc causes a flare at a few times 104 s. The break time, flare time and total flare fluence show correlations, which owe their origin to a single parameter that determines the timescales present in the system, namely the orbital period of the binary system. Furthermore, we show that the properties of the flares are consistent with those of the late-time flares observed in X-ray light curves of some long-duration gamma-ray bursts.