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Measurements of anisotropic flow coefficients (vn) and their cross-correlations using two- and multi-particle cumulant methods are reported in collisions of pp at s√=13 TeV, p-Pb at sNN−−−√=5.02 TeV, Xe-Xe at sNN−−−√=5.44 TeV, and Pb-Pb at sNN−−−√=5.02 TeV recorded with the ALICE detector. These measurements are performed as a function of multiplicity in the mid-rapidity region |η|<0.8 for the transverse momentum range 0.2<pT<3.0 GeV/c. An ordering of the coefficients v2>v3>v4 is found in pp and p-Pb collisions, similar to that seen in large collision systems, while a weak v2 multiplicity dependence is observed relative to nucleus--nucleus collisions in the same multiplicity range. Using the novel subevent method, v2 measured in pp and p-Pb collisions with four-particle cumulants is found to be compatible with that from six-particle cumulants. The symmetric cumulants SC(m,n) calculated with the subevent method which evaluate the correlation strength between v2n and v2m are also presented. The presented data, which add further support to the existence of long-range multi-particle azimuthal correlations in high multiplicity pp and p-Pb collisions, can neither be described by PYTHIA8 nor by IP-Glasma+MUSIC+UrQMD model calculations, and hence provide new insights into the understanding of collective effects in small collision systems.