Blazars make up the largest fraction of Fermi-LAT-detected sources of high-energy gamma-ray emission. At the same time, their emission is known to be highly variable throughout the electromagnetic spectrum. With hints of their highest fractional variability in the radio regime being present at the highest radio frequencies, monitoring blazars at millimetre wavelengths will be one of the key science programmes of the Africa Millimetre Telescope (AMT). Against this background, we study the expected science performance of the AMT based on a sample of 324 gamma-ray blazars with well-modelled spectral energy distributions, taking into account dependencies on likely telescope sizes and locations.