Most of the effects on that site are on this sites tutorial section.
First they have some simple animation, just draw. Then they tween the box edges inward, manual tween would be easier, but it could be programmed. Then they have the growing plant, you could use masks, or that Adobe program I forget. Then they have a few more detailed animations, just draw. Then they have a couple perspective changes on a box so it looks like its 3d, theres a tutorial on that here and you can do much more than look at it. Then they do some flashes of black/white… frame 1, white, frame 2, black, gotoFrame(1).
