I used to be on a 54cm FXE and am a tiny bit taller than you. However, my legs are a bit short for my torso, so the stack was alright, but I was using a 130mm stem to get the right amount of reach. So reasonably speaking, I probably should have been on a 56cm frame at least. Still really enjoyed it though, and used the bike both for commuting and long rides.
Hm, I think the frame is really designed more for the use of a drop bar, as far as I can tell. I had that 130mm stem, and then an Easton bar with an additional 85mm reach. I think you are likely to find this a rather "short" setup with that flat bar - but a test ride will tell!
I used to be on a 54cm FXE and am a tiny bit taller than you. However, my legs are a bit short for my torso, so the stack was alright, but I was using a 130mm stem to get the right amount of reach. So reasonably speaking, I probably should have been on a 56cm frame at least. Still really enjoyed it though, and used the bike both for commuting and long rides.