ABSTRACT Sgr A* exhibits flares in the near-infrared and X-ray bands, with the luminosity in these bands increasing by factors of 10–100 for ≈60 min. One of the models proposed to explain these flares is synchrotron emission of non-thermal particles accelerated by magnetic reconnection events in the accretion flow. We use the results from particle-in-cell simulations of magnetic reconnection to post-process 3D two-temperature GRMHD simulations of a magnetically arrested disc (MAD). We identify current sheets, retrieve their properties, estimate their potential to accelerate non-thermal particles, and compute the expected non-thermal synchrotron emission. We find that the flux eruptions of MADs can provide suitable conditions for accelerating non-thermal particles to energies γe ≲ 106 and producing simultaneous X-ray and near-infrared flares. For a suitable choice of current-sheet parameters and a simplified synchrotron cooling prescription, the model can simultaneously reproduce the quiescent and flaring X-ray luminosities as well as the X-ray spectral shape. While the near-infrared flares are mainly due to an increase in the temperature near the black hole during the MAD flux eruptions, the X-ray emission comes from narrow current sheets bordering highly magnetized, low-density regions near the black hole, and equatorial current sheets where the flux on the black hole reconnects. As a result, not all infrared flares are accompanied by X-ray ones. The non-thermal flaring emission can extend to very hard (≲ 100 keV) X-ray energies.