Quantifying the variability, measured as the root mean square (rms), of accreting systems as a function of energy is a powerful tool for constraining the physical properties of these objects. Here, we present the first application of this method to optical spectra of low-mass X-ray binaries. We use high-time-resolution data of the black hole transient V404 Cygni, obtained with the Gran Telescopio Canarias during its 2015 outburst. During this event, conspicuous wind-related features, such as P-Cygni profiles, were detected in the flux spectra. We find that rms spectra are rich in spectral features, although they are typically morphologically different from their flux counterparts. Specifically, we typically observe absorption components in correspondence to the presence of emission lines in the flux spectra. Similarly, when analysing segments with significant variability in the optical flux, P-Cygni line profiles appear inverted in the rms spectra (i.e., enhanced variability in the blue-shifted region, accompanied by a decrease in that associated with the red component). We discuss the possible origin of these features, which resemble those found in other objects, such as active galactic nuclei. Finally, we highlight the potential of this technique for future searches for wind-type outflows in accreting compact objects.