I agree with everyone who suggested patterned shirts. They help from the front quite a bit.
Also, this is rather cliche, but confidence can play a big role as well. I never would have believed this until I experienced it myself. If you're self-conscious about your chest, tugging on your shirt, and hunching about, it's going to draw more attention to it. Prior to surgery I was unable to bind as I injured myself doing so, and I have a C cup, so I wore a sports bra from May 2013-March 2015. And yeah, you could see that there was a lump there. I looked like I had some thick manboobies lol. For a while I was terrified that it would out me/arouse suspicion/make me a target. But none of that really happened. I started my new job right in the dead of summer, and I literally could only wear these loose/thin shirts that made the chest quite apparent with the bra otherwise I'd probably have gotten heat stroke. I was convinced it would be an issue and that people would notice, think I was female, or ask questions. None of that happened, it was a complete non-issue.People said things that were strictly penis-related, as if I had one, and made reference to my upbringing as if I was cis male. When I did out myself to a girl I liked, she said "but you don't have boobs?" and poked my chest. o.O She didn't even realize they existed until she touched them. And there's one girl I spent like 30 hours a week with, and have for the last 8 or 9 months, and she only noticed that I was wearing a bra when I had no choice but to change into this white shirt after an incident...she began to laugh hysterically and said "is that a bra? Why do you have to wear a bra? omg take that off they can't be that big." That's after hundreds and hundreds of hours in close quarters with this woman, doing all sorts of activities with her, hugging her, being pushed by her (lol), etc. The only time I ever had anyone comment on my chest was in airport security where twice I had officers think the lump was "suspicious" and quickly pat it down. This was in redneck American cities and no one ever gave any indication that they thought I was trans even after patting the chest.
I like to share those stories because I know how it feels to be a big guy and to feel like you have these mountains to hide, and to sometimes go to the point of making yourself uncomfortable in order to do so. My advice is find shirts you like, whether they're buttoned, patterned, whatever, and then just let it go from there an try not to stress over anything that may be visible to you. Chances are no one will notice or care.