I bought the books for my kids this christmas.  How do I claim them on here so we can use them also on our Tablets?  It would be cool if I could claim them on Roll 20 or Fantasy Grounds as well, so I can use the material I bought in any of these formats.  

You can not. Physical books and digital resources are separate products and need to be purchased independently. That may change in the future, but there is no reason to think so. It is a common complaint with no resolution.

I’d add if you buy them digitally here, it doesn’t transfer to roll20, or anywhere else. You need to but it at each place you want to use it. 

Think of it like game platforms. If you buy a game for PC, you wouldn't (necessarily) expect a PS5 and Xbox Series copy of the game for free.

Physical, DDB, roll20, etc. They are all separate platforms that require a different purchase each.

This has come up so many times that there is a sticky thread on the Feedback page Here if you want to take a look. It may answer any questions you may have after reading the responses above.