Any ideas on how to get this effect?

This clip caught my eye, does this begin in 3d?

https://pixabay.com/videos/intro-leon-51802/

While it looks like it was made with Houdini (just a personnal feeling), it might indeed be made again in a 3D scene, using the shape of the lion... Of course, it wouldn't be a piece of cake but if you have the whole lion as a 3D model, you could start having him "wear" fire and other particles on it I think

Looks like particles emit from the geometry into a turbulence field, doesn’t seem to be very complex sim.

It does look like a reasonably basic fluid simulation, could be FumeFx, Houdini, Maya or Blender.

As stated above the geometry of the lion being the emitter.