Find a single-breasted trench coat -- a double-breasted coat will draw even more attention to your chest, which you don't need -- with long, fitted sleeves and that falls to mid-thigh to elongate your body.
Get a trench with a waistbelt to help define your waist.
Wear the trench buttoned up all the way, or leave a couple of buttons at the top undone. The farther up your coat you button, the longer and leaner your body appears.
Wrap the belt around your waist snugly and tie it in place at the front, slightly off to the side. Without a belt around your waist, a large chest would make your body look larger than you actually are, because there isn't any definition between your chest and waist.