Distorting textures with flow maps

I tried FlowMap Painter, but whatever I do, it either reduces the strength, or completely messes up the shape.
@TheJamsh: If it’s not too much trouble, I’d like to know how you make them in Maya/Houdini.

Using the one I posted provides about 3/4 of the effect I want, so if there’s no alternative, I’ll go with that one instead.