So I know you asked for the ladies to give input, but from someone on the other side of the equation, yes it can cause gas.  It depends on the intensity, because if it is PSE style greek and there is lots of full extraction followed by full and fast insertion, it is going to push some air up there. Similar to swallowing air when eating and then feeling burpy.  

The harder and faster you and your partner speak greek...the bigger the "hiccups" you might have in your conversation!  

Maybe the ladies have a technique for fixing this, but does it not sometimes happen during normal "non-greek" sessions when the intesity is high and things dont stay totally inside?

Might be nothing you can do about it for the hard-core sessions.  Honestly, while it may be embarrising for you, as a guy I am far more concerned with the smell than the sound.  

Hope I was at least a little helpful

The sex act is essentially an air pump.  Whether its vaginal or anal - there's going to be air that gets trapped. We're all adults here (well, maybe yours truly excluded, but the rest of you are.)  When it happens I usually apologize to the lady for forcing air insider her rather than ignore it or wait for her to say something.  You gotta laugh at it - the human bodies are funny at times.

My favorite position for greek is missionary and Me on top. I dont experience any gas afterwards. Usually doggy position will make the female have a lot of air up there.

I've never tried Greek but I'm guessing air can get trapped up there, the same way it can with vaginal sex.  You should probably make sure to eat lightly before a Greek session, that way, if you end up gassy, it won't be smelly too (hopefully) lol.

This is exactly why It's not something I do with a lady. Too many things can go wrong. Besides wearing a cover during greek is a waste in my opinion. I have done it the past with my SO but again there is so many things that can go wrong. One girl I used to date was a pro at it. It can be enjoyable but I'm not sure I could with a provider. HidingMyName there is nothing to be embarrassed about.