That is an amazing piece of motion graphics work. Of course, a lot of that was done with actual footage of ink and smoke, but you could fake a lot of this with AE too.
There's a tutorial on the cow that's been here for 8 years that should point you in the right direction. http://library.creativecow.net/articles/polevoy_george/flowing_title.php
You would want to animate it differently and use a different kind of layer for your distortion layer (one with more detail), but the tutorial should point you in the right direction.
I used a similar technique for the very end shot on my demo reel. My resume and demo reel graphics all feature a yellow background with blue splatter so I had some text at the end of my reel transition into splatters.
I created two compositions and each one had a layer with some fractal noise. They were at different scales and other things. Do this to taste. For my purposes I made sure nothing was darker than 50% grey by putting a layer at 50% grey set to the blending mode, "Lighten". You may not need that for yours.
I put both of those comps into my main comp. Turned the eyeball off because you don't need to see these.
On my title layers in my main comp I put four instances of the distort>displacement map effect. 1 and 3 were referencing the larger fractal comp while 2 and 4 were referencing the smaller fractal. I tied the max horizontal and max vertical displacements of instances 2, 3, and 4 to the value of the first instance. That way I would only have to keyframe one of them and all the others would follow.
Then I put a blur and sharpen>compound blur that tied the the larger of the fractal layers and keyframed it up from 0.
- The Great Szalam
(The 'Great' stands for 'Not So Great, in fact, Extremely Humble')
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Thank you so much for the advice it really helped.
I am still busy on this project and I will post what it looks like as soon as the money is in the bank.
I have to apologize for not getting back to this post sooner,
The tutorial is, .... (What the hell) and then in the end I used a combination of this and the Andrew Kramer's (video Copilot.net) Disintegration tutorial.