We flown AC a number of times.. They provide a little better than grocery store plastic bag to put your car seat into.. then you tie the plastic bag like a glad garbage bag.. then they put a fragile sticker on it..

If going to US, you take the car seat in with you through customs, and after inspection you put it on a belt with the rest of the fragile stuff. We always check in our car seats.

We bring our stroller and have checked at the gate.