I flew the day after surgery. Don't think it caused any problems but my face was swollen, I looked a bit downs syndromey. The airport secuitt wanted me to remove my hat so I had to go to a private booth to do that and show them why I was wearing my hat. That was in Belgium last summer which was on high alert due to terrorist attacks there
I flew the day after surgery which people recommend due to swelling, however I did not experience any swelling. Personally, if I had to do it again, I'd stay local as long as possible then travel. Each day your grafts get more and more set up to day 10. If you can chill in the area for 5-7 days postop, it may be ideal.
There is mild donor area pain, and you feel like you are wearing a helmet on your head for the first few days, but there is no significant discomfort.
For both FUT and FUE you can fly out the next day BUT it is never a bad idea to stay in town an extra day in case you have any issues or problems. You may be feeling pretty beat up and a day in a hotel watching tv is not a bad idea before a long flight home.
I flew home the next day before the swelling really set in . I had a fresh dressing and bandage over my donar area .
To be honest I did not give a toss how I looked to others at the airport ect ....as my mission was to get home asap and start the resting and healing process, which is best done in familiar surroundings.
In fairness this was only a 2hr flight ! A Long haul flight might mean it's best to stick around a few days in the location you had the operation.