We report the first detection of a linear correlation between rms variability amplitude and flux in the Ultraluminous X-ray source NGC 5408 X-1. The rms-flux relation has previously been observed in several Galactic black hole X-ray binaries (BHBs), several Active Galactic Nuclei (AGN) and at least one neutron star X-ray binary. This result supports the hypothesis that a linear rms-flux relation is common to all luminous black hole accretion and perhaps even a fundamental property of accretion flows about compact objects. We also show for the first time the cross-spectral properties of the variability of this ULX, comparing variations below and above 1 keV. The coherence and time delays are poorly constrained but consistent with high coherence between the two bands, over most of the observable frequency range, and a significant time delay (with hard leading soft variations). The magnitude and frequency dependence of the lags are broadly consistent with those commonly observed in BHBs, but the direction of the lag is reversed. These results indicate that ULX variability studies, using long X-ray observations, hold great promise for constraining the processes driving ULXs behaviour, and the position of ULXs in the scheme of black hole accretion from BHBs to AGN.