If it's synthetic DO NOT use any oil based products on it. You'll completely ruin the saddle if you do.
The OP stated it wasn't a leather saddle, so why would any of you recommend oiling it or using saddle soap?
Synthetic saddle flaps can and do squeak if the stirrup leathers are rubbing, especially if the leathers themselves are synthetic. It's just the nature of the beast.
OP, there's not a lot you can do about the squeaking. My Wintec flaps squeak too, when I wear my tall boots. They don't squeak from the leathers, though.
I do not really think of it as synthetic though, it probally is synthetic but I just call it fake leather. :P
Here is a few photos even though they're not very handy.