Not a lawyer (but I am an independent musician), so this is a layman's understanding:
I don't think it's been tested in court. I think a lawyer arguing in favor of it being fully legal would argue that it's fair use and causes no demonstrable harm to the copyright holder. I think a lawyer arguing against it would say that it constitutes an unauthorized broadcast of copyrighted material, violates distribution licenses, etc. I think the first lawyer would have the more reasonable argument, but I think the second lawyer would be backed by significantly more money, and generally whoever is willing to spend more money on lawyers eventually wins.
So here's how I'd look at it:
1) If you edit together your music from existing recordings, you are PROBABLY safe. In the extremely unlikely event that a copyright holder takes issue, the first thing they'll do is send you a Cease and Desist letter; if this happens (which it almost certainly won't), it would be wise to comply with the C&D, rather than fighting it in court.
2) If you want to go the extra mile and make absolutely sure that what you're doing is legally permissible, find somebody who does authorized covers, or who does original floor music. Jumptwist and Energym are the first two who jump to mind, but there are others.
(Side note: anything from ocremix.org can be used legally; their terms of use explicitly allow for this sort of thing)
3) If the copyright holder has a litigious reputation and their net worth has the letter "b" in it, you probably shouldn't advertise to them that you're using their music. For example, if your routine music is edited from the original recording of a Disney song, maybe don't tag Disney when you post the routine on instagram.
EDIT
4) ...however, if the track is by an independent artist, you might consider tagging them on social media and asking them ahead of time if they're cool with it. If they're with some big record label, they probably don't own the recordings; however, if they're just self-publishing their stuff on bandcamp, odds are they own the recordings and would be thrilled with their work being used for routines.