There are blocks to set up the Kongregate API and to report scores. They can be found under Game->Kongregate.
As for badges, Kongregate assigns them based on their own criteria. I do know that your game needs a high rating (I've heard 3.85+) and probably a certain number of plays as well. After that, they can only award badges based on the scores you report, so make sure your report any statistics you think may make a good badge!
