After his FR year, he should go to Duke. That will best showcase him in that one year to the NBA. He should put the mission on hold and make a run at it.
BYU doesn't need him for only one year.
If Frank is going to stick to his plan to graduate early and leave on a mission then he should do as planned and sign with BYU. After his mission, he can decide what's next. Play a year or two and see if the NBA is interested.
That way he fulfills his mission dream, has the benefits of attending BYU and can still play in the NBA if it works out.
Stanford is not as good a choice in either case, in Frank's situation. His mom may see Stanford as the most prestigious and the big buck education for free. Obviously, there is something to be said for that. Fine, with his NBA money, he can eventually go to grad school there.