Hi Cathy,
I think it's a natural thing for caiques - they shouldn't really need training for that. I wouuld encourage him by getting him a tent and a ball. That's how Jamie got into it. She especially loves it when she has a piece of blanket (fleece in it) - see pictures below

And she loves it when I put my hand in the tent so that we can wrestle.
And here are more "tent" pictures if you would like to have a look:
http://www.nvan.com/kate/JamieTent/home.htm
You can also encourage it when you play with Yankee. For example, Jamie loves to play on the floor with me. One of the games we play is "I'm going to get your toes). I move my hand on the floor and say "I'm going to get you" and I touch Jamie's leg/toes and then quickly move the hand back. Jamie tries to hop onto my hand on the way back. I let her and we often finger wrestle. In the wrestling, I touch her all over and she often flips on her back (because shw wants to use both legs for wrestling). Sometimes I flip her over on the floor (or on my lap) when wrestling. She seems to enjoy it . Have a foot toy handy and give it to Yankee when you flip him over. Caiques generally love to play with foot toys on their backs.
Your baby is pretty young and he is still getting used to his new environment. I beleive that Jamie started playing on her back a few weeks after I got her. Don't push Yankee too hard - let him get comfortable and once he is, you can start with positive reinforcement training. He will probably show you tons of his own tricks even without being trained
Tani Robar has excellent traiining videos. The website is:
http://www.parrottricktraining.com/
I have used the video and Joey has learned tons of tricks, based on Tani's technique. I taught Jamie some as well.
Kate