Not that they would care, or that the constitution means anything to them...
On the other hand, this sounds like a higher-profile prisoner with access to good legal representation. I would think that, if they actually tried to do that, the prisoners' lawyer would figure it out eventually, and a court would most likely take a dim view of such a practice.
I'm not sure if they've ever actually done that, though. It sounds like they might have kept some problem inmates tied up in pointless transit maybe for a week or three. Doing it perpetually sounded more like speculation than something they've actually done, or could realistically pull off.
You'd have to ask a lawyer, probably one who practices federal criminal law, how such a thing would actually work, but I'm going to guess that if your problem is that the BOP keeps transferring you endlessly, then a lawyer could make a case for filing some kind of suit in almost any jurisdiction, and so you can take your pick of judges and courts.
Overly cynical is how the world works.
CIA Whistleblower John Kiriakou was threatened with permanent con-air for complaining to the press about prison conditions. https://www.documentcloud.org/documents/1018653-john-kiriako...
Living shackled on a plane or bus transferred from prison to prison for years sounds like a nightmare