I did this quite a bit last pregnancy, mostly business trips. The only time it was difficult for me had nothing to do with flying - but the terminal didn't have elevators and I was about 7 months along and had a very heavy suitcase that I had to lug up and down the stairs. Down was ok, but it was a one day trip (suitcase had FRCs, steel toed boots, hard hat, laptop, etc) and after a very long day going up those stairs almost killed me. I ended up writing a nasty letter to the airline/airport about the whole first floor being handicapped parking and what about those who are not fully handicapped but are not necessarily capable of lugging stuff up the stairs, etc.
Honestly, flying was more of a pain after baby when I was pumping. I had to pump in a public restroom (GROSS) and having to declare it and let them swipe test strips on the outside of all the bottles a few times. It was a huge pain.
Either way, the actual flying part was totally fine. I'm flying to Cancun in December and I'm only worried about the food/drinks in Mexico and finding a swimsuit. No concerns about the flying part here.
Good luck!
Re: How many had to fly while pregnant and how many times?
DS: Born 5-17-16
Obviously you can't fly after 35ish weeks and you might feel more sick on an airplane in the early weeks, but other than that you're good :-)
I am flying across the country next week. I am kinda nervous as I am 12 weeks now, but I am sure it will be fine! Just going to get up and walk to use restroom a few times to get the blood flowing.