I ran into this problem while trying to make animated dance floor patterns for the nightclub level. At first I thought about using Substance Designer for this but its animation tools are mostly not documented and pretty complex from the look of it. I've downloaded a pack of animated noises, mixed them, got some decent…
You can set up an orthographic camera with a texture-friendly frame size (1024² for example) and make the animations in Maya or Blender with morph targets, animated materials etc. Then render as an image sequence that you import as an animated texture into the game engine. EDIT: Just to prove my point. With Shape Keys in…