I traveled over Christmas with my sun conure and it went well. It was stressful for me, but I think it was my nerves and not because anything was going wrong. I had the maximum size travel cage, and it was a real PAIN to get under the seat in front of me. So, make sure to get an isle seat. I had to switch with people, because I just couldn't get it under there in the window seat. See if you can get a direct flight, otherwise your bird will probably need to stretch his wings between flights. We had a 3 hour layover and it was great. We found an empty corner and ate lunch and played the whole time. He was exhausted by the next flight. Also, make sure to pack lots of toys and treats with you to appease at any minute. The last thing you want is to have a screaming bird on the flight. Darwin actually slept through all 4 flights, which worked great. I put his hanging tent in the travel cage and he snuggled in it and went to sleep.
As far as security goes, both runs through security were fine for us. I took Darwin out (he is clipped though) and we walked through together. The first time I let him perch on me and he pooed (dont suggest that--they freaked out and got disinfectant). The second time, I held him close to my body (kind of cupped him to me), and we walked through like that. I think this was less stressful. But it was fine, and right after we walked through they gave me the travel cage back. Everyone was very interested in him too.
Here is a thread about a few of us that traveled over break with birds. And a few more tips that I am forgetting!
Traveling via Airplane