It's an all-Skyteam itin, just two airlines and two connections....Can't imagine it being a problem. You obviously don't have to clear customs before PRG, either.
I guess that's a bit late for you now, but if I were you (and assuming you are not interested in collecting segments) I'd fly OK from BHX. The latter is less than 100 miles away from BRS and offers two nonstops to PRG by CSA and probably a couple of others by lo-cos every day.