I've been to Green Island several times, not for kiting, but for diving and snorkeling.
It's a great place - for moms and their screaming kids!
But on the rear of the island opposite the pier side, there is a good take off spot, with a sandy bottom. After about 2 metres in, it's all reef. It's the only place you can kite (take off) from, as you may get arrested doing it near the tourist, pier side. So once you're up, keep away from being tempted to circle the island or anything like that.
Booties are a must!
Watch out for a left over pillon and pier on the southern side of the Island closer to the ferry pier, as it sticks out of the water on low tide. But since you won't go there, you should be ok.
Usual SE trade winds. If Yorkey's Knob or Palm Cove is blowing so will Green Island. That's usually the marker I would go for.
Believe me, I've been there without a kite and wondered the same thing, kicking myself for bringing one over.
You can also ask Cairns Kiteboarding what they think.
Cheers