Hey,
You will have to sign out of that Microsoft account via the Microsoft store and then sign into your sons account. All Destiny data is associated with that platform account therefore if you sign into your sons Microsoft account on the Microsoft Store the launch Destiny it should have his data.
English
-
Microsoft Store didn't work. I revoked access do D2 from my account - didn't work. Resetted a game (w/o installing it once again. Still no luck. But when I've logged out from XBOX app it worked. I'll leave it here as solution. Thanks for direction :)