Cross-section measurements for the production of a (Z) boson in association with one or two photons are performed using proton-proton collisions at a centre-of-mass energy of 13 TeV. The data used correspond to an integrated luminosity of 139 fb(^{-1}) recorded by the ATLAS experiment. The measurements are performed using the leptonic decay channels of the (Z), and in a phase space region where the dominant photon production is from the incoming proton constituents, rather than off the leptons from the (Z) decay. The integrated fiducial cross-sections are measured to a precision of 3% and 12% for (Z)γ and (Z)γγ respectively, making these the most precise measurements of these processes to date. The cross-sections are also measured differentially and are compared to predictions from state-of-the-art theoretical calculations and Monte Carlo generators.