Is there something in the FA rules about a player going from the U21s to the senior team and not being able to go back to the U21s? I thought I heard somewhere that they would want to hold Kane back and have him continue to play for the U21s since they have been doing good and have a good chance at going far in the U21 Euros.
No, there's nothing like that. Quite often once a player becomes a senior they think they're too good to go back to the youth set up though. There's also the case that during the European Champions or World Cup there is also youth competitions happening at the same time, so the player/manager can only use him in one.
It's always been a problem in England that we rush youth through to the senior side as quickly as possible, the youth then don't play in youth world cups and so are shit in senior tournaments due to a lack of experience.