I flew international long haul at 34 weeks from London to Perth and have also flown at 37 weeks from Karratha to Perth (only around 2.5 hrs) and was fine. I had letters from docters etc both times and my pregnancies had no complications.

Turbulence didnt bother me at all but I did find that despite best efforts of drinking lots of water, wearing support stockings and doing little leg excercises by the time I got off the plane I had swelled up and this swelling pretty much then lasted right thru to birth and didnt go down.