Elliptic flow measurements from two-, four-, and six-particle correlations are used to investigate flow fluctuations in collisions of U+U at sqrt[s_{NN}]=193 GeV, Cu+Au at sqrt[s_{NN}]=200 GeV and Au+Au spanning the range sqrt[s_{NN}]=11.5-200 GeV. The measurements show a strong dependence of the flow fluctuations on collision centrality, a modest dependence on system size, and very little if any, dependence on particle species and beam energy. The results, when compared to similar LHC measurements, viscous hydrodynamic calculations, and trento model eccentricities, indicate that initial-state-driven fluctuations predominate the flow fluctuations generated in the collisions studied.