Also for what it's worth, I've flown a lot while pregnant (MFM and hospital a flight away from our home), the latest I flew was 35w, and flight/gate attendants never said boo to me about it... and I'm tiny so I look enormous pregnant (and actually was extra big because of extra fluid).
Obviously since I was going to see my doctor flying was fine by my them (short 1hr flights)- but just wanted to share my experience at the airport- no one seemed to care, though I suppose that might be different in other countries and a letter would give you more piece of mind.
We also always drank lots of water, and on longer flights made sure I walked around frequently to keep blood moving around.
2008-Our Baby Girl, PTL born too early at 30w6d, Fought so hard... Forever Loved & Missed
2010- Lil' Bro, Pre-E at 29 weeks... Induced at 36w6d, Born 37w
2012- Lil' Sis, Super-imposed pre-e at 25 weeks, PTL & GD at 35 weeks, Evicted 36w