if you goal is to do the same thing that your video ref, i would use a mesh with an animated noise map in the displacement, with a xray shader, few passes an a clever comp it should give you good results. or a softbody planar...
i have check your fumfx fire, be careful to the smoke, there is way too much. fire don't really do that much smoke it is more the things burning around not the flames themself or just the tips. look some ref.
good luck