We discuss four important aspects of 1.5 MeV Au2+ ion-induced flux dependent sputtering from gold nanostrcutures (of an average size 7.6 nm and height 6.9 nm) that are deposited on silicon substrates: (a) Au sputtering yield at the ion flux of 6.3x10^12 ions cm-2 s-1 is found to be 312 atoms/ion which is about five times the sputtering yield reported earlier under identical irradiation conditions at a lower beam flux of 10^9 ions cm-2 s-1, (b) the sputtered yield increases with increasing flux at lower fluence and reduces at higher fluence (1.0x10^15 ions cm-2) for nanostructured thin films while the sputtering yield increases with increasing flux and fluence for thick films (27.5 nm Au deposited on Si) (c) Size distribution of sputtered particles has been found to vary with the incident beam flux showing a bimodal distribution at higher flux and (d) the decay exponent obtained from the size distributions of sputtered particles showed an inverse power law dependence ranging from 1.5 to 2.5 as a function of incident beam flux. The exponent values have been compared with existing theoretical models to understand the underlying mechanism. The role of wafer temperature associated with the beam flux has been invoked for a qualitative understanding of the sputtering results in both the nanostructured thin films and thick films.