Most sites use the style 2001 for men, so that's probably the relevant style/size chart if you haven't found a chart.
As you've found, American Apparel is a slim fit shirt. The general advice is to move up a size if you like a looser cut. That gets trickier if you're between sizes. I'd only be speculating, but I think unless you like your clothes
very loose, you probably want an L rather than an XL. American Apparel is smaller than brands like Gildan, but not a full size smaller. If you're between an M and an L in Gildan, it's even possible than an AA L would be just right.
American Apparel is a flattering cut, providing it's not worn absurdly tight (close to the body, yes - just not
tight). A lot of us in this world have body image issues (myself included), so you might not feel comfortable wearing the shirt as a close fit. They do look good though, if you can bring yourself to wear it - might be worth it
