This paper describes the measurements of flow harmonics v₂-v₆ in 3μb^-1 of Xe+Xe collisions at √^sNN=5.44 TeV performed using the ATLAS detector at the Large Hadron Collider (LHC). Measurements of the centrality, multiplicity, and PT dependence of the v_n obtained using two-particle correlations and the scalar product technique are presented. The measurements are also performed using a template-fit procedure, which was developed to remove nonflow correlations in small collision systems. This nonflow removal is shown to have a significant influence on the measured vn at high pT, especially in peripheral events. Comparisons of the measured vn with measurements in Pb+Pb collisions and p+Pb collisions at √sNN=5.02 TeV are also presented. The v_n values in Xe+Xe collisions are observed to be larger than those in Pb+Pb collisions for n=2, 3, and 4 in the most central events. However, with decreasing centrality or increasing harmonic order n, the v_n values in Xe+Xe collisions become smaller than those in Pb+Pb collisions. The v_n in Xe+Xe and Pb+Pb collisions are also compared as a function of the mean number of participating nucleons, (N_part), and the measured charged-particle multiplicity in the detector. The v₃ values in Xe+Xe and Pb+Pb collisions are observed to be similar at the same (N_part) or multiplicity, but the other harmonics are significantly different. The ratios of the measured v_n in Xe+Xe and Pb+Pb collisions, as a function of centrality, are also compared to theoretical calculations. © 2020 CERN.