how i carry my jackets is to fold it length wise along the spine (typically fold it INTO itself -- meaning flip inside out and insert 1 sleeve into the other), and then once more the other direction so that sleeves are folded at the elbow.
if the jacket doesnt have high linen content, and the isnt absolutely and utterly compressed in luggage, then it does not wrinkle. thats whether i put it in a suit bag or not; into carry-on or check-in; etc.
for your jacket to look like that it's got to have been mushed up (perhaps by other content) with lots of pressure applied to it