After a question was recently closed the poster of said question started downvoting posts of everybody participating in the closure of his question.
Is such behavior considered appropriate?
No, it's not. Report it (like you did with this thread), and the mods will take a look. It's been a while, but I recall there being a suspension category for this kind of behavior. He certainly wouldn't be first to get a time-out for retaliatory voting.
On a related note, this type of poster is just another reason to think twice about commenting on bad, downvoted questions. You end up becoming the target of some asshole's misplaced anger a lot more often than anything constructive comes of it. Better to just downvote, (and/or) vote to close, shake your head at the fail and move on.