I was told by my mw after trying to push my dd out for 2 hrs that I had a flat pelvic bone. I had been pushing in bed on my side and sitting up on the toilet with no luck (didn't help that dd was also posterior). Oddly enough, once I flipped onto my back, I started to make progress. It could have just been the movement from side to front that caused dd to turn face down, though, making it easier to push her out.
I plan to push this baby out in a squat if at all possible. It just makes sense to me.
Anyway, don't worry too much about it. Just from this small sampling, it seems like flat pelvic bones are pretty common. The baby will come out. Probably the most important thing is to listen to your body when you're birthing and push in whatever position feels right to you.