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 minutes. 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 PIC 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 {gamma_e} <~ 1e6 and producing simultaneous X-ray and near-infrared flares. For a suitable choice of current-sheet parameters and a simpified 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. 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.
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