New measurements of elliptic flow from two- and four-particle correlations are used to investigate flow fluctuations in collisions of U+U at root s(NN) = 193 GeV, Cu+Au at root s(NN) = 200 GeV and Au+Au at several beam energies. These measurements highlight the dependence of these fluctuations on the event shape, system size and beam energy and indicate a dominant role for initial-state-driven fluctuations. These measurements could provide further constraints for initial-state models, as well as for precision extraction of the temperature-dependent specific shear viscosity eta/s(T).