This quick-change stuff has floored me, ever since being introduced to it in a Lincoln Rhyme crime novel (The Vanished Man, by Jeff Deaver). I've seen several performances, and even knowing how it works doesn't reduce the wonder!
I saw this act at a Michigan State Basketball game last winter. Their act is much longer than it was on the AGT show. It was AMAZING - think of twice as many outfit changes as was seen on the talent show.
Each outfit looks like a dress or a suit, but it's really a very thin fabric, possibly silk, that is coloured and cut to look like a dress or suit. With a tug in the right place the whole layer is removed and stashed in the object covering the artist. The illusion is getting the audience to not notice the change. That's where the skill lies.