your getting dangerously close to a known source of controversy here. i dont know anything about aac files, IF i am correct theyr apples version of a lossless file.
now as far as the difference between 320kbps mp3 and flac goes. there definitely IS a difference, the question is whether or not you can hear it. once, mp3 were compressed badly and the differences were obvious. today, with new algorithms and what not, youd need good ears to tell the difference between an mp3 and a flac file, so long as the original recording was good to begin with.
theres even a thread somewhere with a blind test that plays you the same song in a different format and you have to guess which is which. the web is full of tests just like these.
now im not taking a stand in either direction. most people around here will tell you to use FLAC files because they are better quality. if you ask me? download an album you love and know very well in both formats and see for yourself if you can tell a difference. if you do, go for the one you liked most. keep in mind, im not sure a smartphone will play FLAC files, mine doesnt (galaxy ace). i dont know about apple or sansa products and what they can\cant play.
and a files format has nothing to do with your headphones. you play the file through your source (phone, ipod, mp3 player, computer, whatever), not through your headphones. theres no format that headphones cant play, only sources that cant play certain formats. it doesnt matter if your using sure, akg or anything else.