My husband just got a cold sore and touched my 2 month old son on the hand after flossing. My baby often puts his hands in his mouth. Can he get it?

Possible. Possible but not not likely. It usually takesore exposure than that.
Not likely. It is remotely possible that the baby will get a herpes infection but very unlikely.
Yes, possibly. If it's a viral lesion, it is potentially transmissible if the baby gets active virus inside his mouth. If the cold sore is of non-viral origin, it is less clearly transmissible.