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 vn 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 vn 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 vn values in Xe+Xe collisions become smaller than those in Pb+Pb collisions. The vn in Xe+Xe and Pb+Pb collisions are also compared as a function of the mean number of participating nucleons, (Npart), 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 (Npart) or multiplicity, but the other harmonics are significantly different. The ratios of the measured vn in Xe+Xe and Pb+Pb collisions, as a function of centrality, are also compared to theoretical calculations.