I also do not believe we will be seeing the Gloucester jewels move away from the family anytime soon.
Definitely not while the current Duke and Duchess are still living, but after they die, Alexander will succeed to the Dukedom and have no need for such a large and valuable collection of jewels. At that point, it is very likely they will be auctioned off to raise funds and pay death duties.
The Gloucesters are not rich by any means and the money will be welcome to secure their futures.