How to animate album art after skipping song?

I tried to use $mi(state) = SKIPPING_FORWARDS$ and linking it to a global switch, but that did not detect the change.

If you mean an animation when you skip a song with a next or previous button, you can create a global switch and after that put a touch action linked to it in the same button where you make the skip action. Create the animations based in this global switch.

What about skipping songs from the default music controls and not a Kustom button? Is there any way to detect that?

If you tried without luck, I don't think so. Kustom apps depends of the information broadcasted by your music app to perform, if the skip action is not broadcasted by the music app, Kustom apps can't act. To be honest I don't see many music apps broadcasting this skip action.