there's no simple way. but there are ways to do each.
i would recommend googling to see if there's something you an do yourself, or check milkman apps tro see if you can implement one or more of his anes.
there isn't much source about AIR for iOS really, especially when it comes to game center or UIActivityViewController
I guess AIR does not support UIActivityViewController by default. There must be an extension anyways? The same for game center.
I'm still not sure what Gaming SDK does in this case.
I always come across milkman apps, and started thinking of purchasing if there is no other solution.