© 2019 American Physical Society. The first (v1fluc), second (v2), and third (v3) harmonic coefficients of the azimuthal particle distribution at midrapidity are extracted for charged hadrons and studied as a function of transverse momentum (pT) and mean charged particle multiplicity density Nch in U+U (sNN=193 GeV), Au+Au, Cu+Au, Cu+Cu, d+Au, and p+Au collisions at sNN=200 GeV with the STAR detector. For the same Nch, the v1fluc and v3 coefficients are observed to be independent of the collision system, while v2 exhibits such a scaling only when normalized by the initial-state eccentricity (μ2). The data also show that ln(v2/μ2) scales linearly with Nch-1/3. These measurements provide insight into initial-geometry fluctuations and the role of viscous hydrodynamic attenuation on vn from small to large collision systems.