I have just set my son up with his own xbox login. Is there a way to transfer his saved...

Unfortunately no. Nothing can be transferred between profiles.

When I bought my minor son his first Xbox, I added the Xbox to my account and had my son sign in there to use it. He is now an adult and I want him to set up his own Microsoft account and move his Xbox to his own account. How do we do this??.

You can easily havr him create his own account and log into his xbox.

He will lose access to his saved games and anything linked to your account. They cannot be transferred to another Microsoft account, nor can his gamertag.

He would essentially be starting fresh on his account.

My oldest son has his own console, his own login, and his own xbox live.

My youngest son has his own console, his own login, and his own xbox live.

The game should belong to my oldest son.

So how does this work? Do I want my youngest son's console to be the home console? Then when logged in as my oldest son on the home (youngest son's)console, download the game to the youngest son's console? Then let my oldest son go back to his console
and have him download the game to that console too?

Then would my oldest be able to play his game on his own console (not the home console) with my youngest son also playing it on a different (home)console, with each kid logged in as themself?

So if I get my son one I can just transfer his login over to new Xbox and he will still be live.

There is unfortunately no way to transfer digital content (games, apps, saves) from one account to another at this time.

However, a workaround is available if you don't want him to log into your account anymore, but still have access to the purchased games while logged on to his own account: set up gamesharing!

On the Xbox One console your son plays on, log on with your account, and set this Xbox as the "Home
Xbox". Log out, and let your son log in with his own account. He can continue to play the digitally purchased games (from your account), and if your own Gold subscription is active, he can play online too.