Have you tried sports bras?
I can usually get my chest to appear flat with three sports bras, two shirts, and slouching.
The bras are too small for normal wear on me (not that I ever wear them other than for binding), and I have to align the elastic parts (at the bottom) where I would like to mash down the lumps, but it works well with two shirts and bad posture.
It probably depends on your chest size whether or not this will work for you, though.