Good question. I know when I first started in 2000, I was told that the f/as for the Dallas Cowboys charters were asked for by name by the team. No male f/as were ever used, or so I was told. (I've also talked with some f/as who worked Cowboys charters. They didn't like them because they had to hand run meal trays even in coach, and the players were always up in the aisles blocking them from getting their jobs done.) I've worked the Veterans charters before. That is voluntary and unpaid. I worked a charter for a crowd of football fans going from Chicago to Jacksonville, Fl for a bowl game several years ago. For reasons known only to American Airlines, airplane and the crew were all STL-based. So, we had a 4 leg charter. The first and the last legs were ferry flights between STL and ORD.
I also have seen charter flight positions out in Open Time on the computer where anyone qualified on that aircraft and available on the day(s) of the charter could pick up the sequence. You can always tell the charter flights because the flight number is 4 digits beginning with a 9--i.e., 9420. I'm just guessing, but I would imagine that on charters for VIPs--such as, the Holy Father--the crews are hand-picked. By what criteria, I have no idea, but I'm sure the company is making every effort to put its best foot (and crews) forward.