I have an aviator harness although I have yet to use it (too cold still) but most birds accept it pretty well. You can let them wear the harness to get used to it and then progress to adding the leash and starting walks.
My dream is to get Arnie to wear hers as she LOVES flying. But she gets really mad if I bring it near her. I've tried the gentle "leave it on the cage, see it's not scary" training, the "I'll just lift your wing to get you used to handling" (she hates that and will squabble) and the "I'll just put your head through it whilst you nibble on some millet". No luck. I've stopped trying with her because it's SUCH a drama trying to train her.
As a result, I'm nervous to start training with Erin... she's a much more mellow tiel but I don't want to upset her.
I'll admit I didn't really 'train' mine to wear it, I just watched the dvd, whacked it on them, and took them outside. They complained the first few times I put it on them but now they just wiggle around a bit and nibble at it. I'm hoping they'll grow out of the nibbling though since I'm paranoid they'll damage the harnesses