If I buy Avast Internet Security download from a third party like amazon can I download the program directly from Avast and then enter the licence key to activate it?
Yes you should be able to download it, using one of the links in the forums - https://forum.avast.com/index.php?topic=210678.0.
I would say your main concern would be the legitimacy of the license purchased, there are many dubious sellers on some of the sites.
Thanks David. Here is the link: https://www.amazon.com/Avast-Internet-Security-Years-Download/dp/B0765CYPKK It’s sold by amazon so I think it would be legit but I don’t know if I should go ahead and buy it.
Not necessarily legit.
Note there have been no reviews as of current yet. See attached below.
No Refunds, No Returns… Caveat emptor - Let the buyer be ware.
(It’s your money.) 
It is now saying this item is no longer available.
I don’t know if this is the seller ‘AVAST Software s.r.o.’ but I rather doubt it is Avast or an Avast Reseller, they wouldn’t run out of products or keys.
Also ‘Download size: 6 MB’ is the on-line setup file, I don’t see anywhere that talks about receiving your license.
Too much doubt here to risk any money on it.