Images from the vicinity of the black hole horizon at the Galactic centre (Sgr A*) could be obtained in the near future with a Very Large Baseline Array of sub-millimetre telescopes. The recently observed short-term infrared and X-ray variability of the emission from Sgr A* implies that the accretion flow near the black hole is clumpy or unsteady. We calculate the appearance of a compact emission region (bright spot) in a circular orbit around a spinning black hole as a function of orbital radius and orientation. We find that the mass and spin of the black hole can be extracted from their generic signatures on the spot image as well as on the light curves of its observed flux and polarization. The strong-field distortion remains noticeable even when the spot image is smoothed over the expected 20 mu as resolution of future sub-millimetre observations.