This may be a stupid question, but fasm outputs "flat" binaries. What's a flat binary compared to a normal one? Does it have anything to do with flat vs. segmented memory models?

yes, it means it's default and only memory model of FASM is flat (pure 32bit).
It is much better than MASM's fooling with useless memory models.

I would say it has less to do with the memory format and more with the 'philosophy' of fasm if you can call it that. Fasm can easily handle multiple segments, be they physical memory segments or segment based binary formats. Fasm does not worry about specific environment requirements, and thus lets you assemble a single instruction, or even none at all without complaining. Thus you can produce 'flat' binary files that contain no header, segment information, etc, which is great because it makes porting/integrating fasm a lot easier and gives you the ability to write small proof-of-concept code, boot sector code, code for different operating systems, position-independant-code, etc.

Thanks for the info guys. It's helped clear thing up for me.