DENIS-P J0041353-562112 is a brown dwarf, with a spectral type of M7.5, which may be younger than 20 Myr. On the basis of its Hα emission-line asymmetry, it has been suggested that the object is accreting material. If it is accreting, it is expected to rotate slowly. This paper reports on several photometric monitoring runs in the RC and IC bands, designed to study variability - such as that due to rotational modulation - of the object. Although there do not seem to be irregular brightness fluctuations typical of accretion, there is cyclical variability which may be due to a bright accretion-related spot. The rotation period is 2.8 h, although a double-wave variation with a period of 5.6 h cannot be ruled out completely. If the shorter period is correct, it is unlikely that the brown dwarf is disc-locked. Substantial flaring activity in the RC band suggests a strong magnetic field.