My experience on East and West Coast with Delta flying with Otto, both times they took me to a closed room and had me hold Otto while they scanned his carrier. These were the only times I ever had his wings clipped for safety, otherwise he's normally full flighted. I do recommend having your birds wings done for the airport stuff.
TSA are usually very nice about it and listen to you when you tell them you have a live bird, especially if it's full flighted. You want to tell them when you're putting your shoes and stuff through the xray. In cabin - you'll want to bring a warm cover both times where I was supposed to put his carrier (under the seat in front of me) it was really cold no matter the season. During flight no one said anything if I had his carrier on my lap. But take off and landing it has to be all the way under the seat in front of you.
Make sure you have the required health certificate from your vet. You will have to go to a special desk to show that vet provided paper, show carrier and pay an additional fee. Hope this is helpful.
Good luck!