Flame structures are sedimentary structures that usually consist of upward-pointing flame-shaped finer-grained sediment tongues that protrude into coarser sediment (like sand). Almost invariably, the ‘flames’ are inclined in a downslope direction (in a paleogeographic sense, of course) — like in these two images from the Precambrian Windermere Group in the Canadian Caribou Mountains.
Flame structures are often interpreted as load structures: the overall higher-density sand sinks into the lower-density underlying shale. That would put flame structures into the category of Rayleigh-Taylor instabilities, which result from density inversion. In geology, one of the most important types of Rayleigh-Taylor instability is related to salt: if buried deep enough, the density of the compacting overlying sediment exceeds the density of salt, and the latter starts flowing upward, giving rise to salt diapirs. Salt diapirs often have mushroom shapes, typical of Rayleigh-Taylor instabilities.
The shapes of the flame structures above actually remind me more of the Kelvin-Helmholtz instability, which is related to shear (that is, different velocities) across a fluid interface, and can occur even if the densities are not inverted. K-H instabilities in the atmosphere can result in elegant clouds. K-H billows are common at the tops of turbidity currents, due to the shear between the static water column above and the moving sediment-laden current below. There is no reason why the instability could not occur at the base of the current as well, if the underlying sediment is still fluid enough, and the current itself is not too erosive.
Here is the classic picture of K-H billows at the top of a density current, from Van Dyke’s Album of Fluid Motion.
Clastic Detritus has more on flame structures.