Time to punch in. Gonna do this will all text. For a Fire vortex variation, I only did some playing it and I didn't take it all the way. I only did enough fiddling to satisfy that it will look decent enough.
Gonna do this on a 256x256 canvas. With the Offset filter, we'll be going by increments of 16 for a total of 15 frames. Most people would think that it's 16 frames because 256/16=16, but the last frame is the same as the first, so it gets deleted.
Start New Doc with 256x256.
First thing to do is make the Magic Layer. This is our tilable pattern that we'll be operating on. You make it by running Filter > Distort > Clouds once, then running Filter > Distort > Difference Clouds enough times to make you happy. Make sure you are using the Default colours - hit 'd' to make sure before you start getting crazy with Clouds/Difference Clouds.
Quick Note: Not a bad idea to run Image > Adjust > Levels (ctrl + l) and bring Output Levels 255 down to 253. If you don't do this, then you'll get pure white artifacts when we add the Colour Burn Mask Layer. Then again, you could save this for later and use a Levels Adjustment Layer, which probably isn't a bad idea so you can do more tweaking while you're at it.
Copy your Magic Layer just in case.
This next part kind of sucks because you don't know how it's going to look until much later down the road. Here's what I tried real quick and was mildly pleased:
Ran Filter > Stylize > Wind using Method: Wind and Direction: From the Right.
Image > Transform > Rotate 90 CCW so it looks like icicles.
Then Filter > Distort > Ripple using Amount: 100% and Size: Small.
Not bad, huh? Now, this is going to be our Second Magic Layer. This is the one we'll be copying and operating some more on. This should stay intact. Copy it and let's continue.
Filter > Distort > Polar Coords using Rectangular to Polar.
Are you starting to see it? Okay, let's add a few things to spiffy it up.
Add a new layer on top of that and set the Blending Mode to Colour Burn. Fill it with pure black. Grab the Airbrush, nice, soft and with pure white, and so some painting. Paint mainly in the middle and stroke outward. This is the Colour Burn Mask Layer. Once you get the feel for how this works, leave touching it up for later.
To colourize it, add a Gradient Map Adjustment Layer. The colours on the sliders should look something like this:
Black - Red - Orange - Yellow - White
Play with it until you are happy. Again, prolly be playing some more with this later.
Now, the middle of the doc will present a problem. It will be a pin hole or something shooting out black and white. Don't want that. Add a new layer between the Magic Layer and the Colour Burn Mask Layer. Paint some white in the middle, maybe even set the Blending Mode to Screen. We'll call this Pin Hole Fix Layer.
Time to get tedious. This is were an Action comes in handy.
Copy Second Magic Layer.
Order to underneath of the pin hole fix layer.
Filter > Other > Offset and use
Horizontal: 0
Vertical: 16
and Wrap Around
Filter > Distort > Polar Coords using Rectangular to Polar.
Copy Second Magic Layer.
Order to underneath of the pin hole fix layer.
Filter > Other > Offset and use
Horizontal: 0
Vertical: 32
and Wrap Around
Filter > Distort > Polar Coords using Rectangular to Polar.
Copy Second Magic Layer.
Order to underneath of the pin hole fix layer.
Filter > Other > Offset and use
Horizontal: 0
Vertical: 48
and Wrap Around
Filter > Distort > Polar Coords using Rectangular to Polar.
Keep doing that. The final Offset to be used is
Vertical: 240.
If you haven't saved yet, now would be a good time to do it. As a matter of fact, you have to save it to move on to Image Ready, which is the next tedious part.
Are you in IR yet with a Bunch-O-Layers Fire Vortex document yet?
Should have the first frame loaded and ready to go. The Layers turn on should be:
The bottom Polar Coords Layer
The Pin Hole Fix Layer
And the layers above that (I've already forgotten the names of them).
Add a frame.
Turn off the current Polar Coords Layer.
Turn on the Polar Coords Layer above it.
Add a frame.
Turn off the current Polar Coords Layer.
Turn on the Polar Coords Layer above it.
Add a frame.
Turn off the current Polar Coords Layer.
Turn on the Polar Coords Layer above it.
Et cetera until you run out of Polar Coords Layers. Theoretically you should end up with a total of 15 frames.
Play it and see what it looks like. Should be spiffy.
A good thing to do right now is to set the Disposal. Select all frames, right click, and choose Automatic.
Save it again if you haven't already.
Now it's time to do all that tweaking that needs to be done. Believe me, with all of the elements running around, there is great potential for variations and what-not. For example, changing the G-Map Ad-Layer can do wonders. Playing with the Colour Burn Mask Layer can give very different looks and feels to it. The things that you do to the Clouds/Difference Clouds is also a good thing to play with. All of these things play together for truly wonderous things.
Heh. Maybe even add that Levels Ad-Layer that I mentioned earlier.
Eventually export the animated GIF. And ave the PSD again, but with a different file version number.
Now, for Flash, I'm not sure how to go about it. Maybe do your initial document at 512x512 and size it down and needed once you're happy with it. Then, save out each frame individually. Then, load them into Flash and Trace Bitmap to vectorize them. I have no idea if vectorizing the individual frames will cut down on file size or not, but I do know that an animated GIF can get big in a hurry.
That's about it from me for now. I'm sure questions will be flying all over the place. Maybe someone will even play with this and post results. Maybe Lil' Bowser will make a guest appearance.
play.fiddle.learn
That's a "toughie" and I really like Erik's tute for the static version. You can easily adapt same to recreate the anigif that Stroker has shown. 
Stroker! I remember that waaaaaay cool image of Lil' Bowser giving pakman the "business"!