Hi,
As long as you aren't showing any signs of any complications (pre-eclampsia, preterm labour etc.) then you should be fine. Most airlines allow you to fly up until the end of your 36th week as long as it's a singleton pregnancy and you have a letter from your care provider stating how far along you are and that there have been no complications in your pregnancy.
I am flying at 33+4 from New Zealand to London - 24 hours on a plane (well, technically two planes). I'm dreading it as I worry I will be horrendously uncomfortable for such a long period of time, but we had plans to go travelling before we found out we were pregnant and we didn't want to cancel them so we're just coming home earlier in time for the baby to be born.
As long as you stay hydrated, move around the cabin every hour or so and wear support stockings (this one isn't necessary, but it's advised) then you should be perfectly fine. Airlines don't like the thought of you going into labour in the air as they have to make an emergency landing, which costs them lots of money. That's why they stop women flying after 37 weeks - not that it is a risk to the mother or baby, but the chance of going into labour is obviously much higher then. The risk of preterm labour is the only risky thing about flying, but even then, flying doesn't cause you to have an increased risk. If it were going to happen it would happen on the ground too, the only problem is it's obviously more risky if you're in a plane instead of a hospital! Flying in a normal pressurised cabin won't harm you or your baby at all.
x