I've seem that video where you had Kili out in your car (well one video in case you have more than one).
As cool as it seems, I don't think I would have mine free in the car.
As much as some could seem to be well behaved and calm, something could easily spook them and then it could mean trouble. Either them flying around and causing you to get into an accident; either them ending up beneath one of the pedals..or there is also the possibility of getting in an accident by no fault of the bird and with them being loose, they could end up more hurt.
To each their own really, but I don't think I would want to risk it. I have them in their carriers and those carriers are buckled in.
As for bringing them on a plane, unless I'll be moving, I don't I'll do it because a) I have too many birds and would exceed my carry on capacity
and 2) given the number I have, it would probably end up being costly.