Stealth

I'm not linking to it because I don't want to create problems for someone trying to go unnoticed and it's not important to have a specific link. It's a common question.

MOST bras make breasts more noticeable. However, sports bras help flatten them out.

Snug tank tops are masculine coded while doing much the same, especially in early stages while breasts are small.

See also: Supporting the Girls

I have been bra free for years and have had short hair, even sometimes bald, and I'm about average height for a man for my country and usually do not carry a purse. I get called "sir" sometimes, most often if someone sees me from the back. I turn around and people apologize for misgendering me.

I think bra straps showing through clothes are a huge part of how people decide who is a woman because, honestly, dresses aren't that common and men sometimes carry a bag of some sort.

You can absolutely downplay breasts without a bra. Wear thick shirts that go up to the neck. It should be dark material and if you go with a T-shirt, those that have stuff printed on the front help trick the eye.

If you are pudgy and wear a baggy shirt and hunch over slightly, your belly may stick out further than your breasts and cause your shirt to tent over them. They may be completely invisible for some time so long as it's not, say, a thin white shirt.

To my surprise, all of the above tricks help substantially even if you start losing the belly. Granted, I'm not trying to hide my gender. I'm only trying to hide the fact that I'm braless because I'm too poor to be able to afford manners in accordance with my mother's extremely upper class expectations.

I will suggest you start with snug tank tops for stealth breast support and GRADUALLY start dressing more androgynously or ambiguously. I know a lot of trans people are in a big hurry to dress like the gender they feel is their correct gender but I feel this actively creates social friction and if you are in a risky situation, it's just a bad idea.

You may also wish to read Being LGBTQ in a Conservative Culture. Be advised it's my unvarnished opinion of some of the things people get wrong and thereby unnecessarily create their own problems. 

No, I'm NOT saying "It's YOUR fault people are transphobic/homophobic." I'm saying "I'm fairly certain some portion of this is avoidable AND you have the most control over YOUR choices, not other people."

Last, the REAL reason I am writing this is to note that my desire to try to work out a nutrition based DIY HRT protocol is partly about stealth. 

I have a serious medical condition and long ago figured out eating chocolate or drinking coffee opens my airways similar to a rescue inhaler without loudly announcing to other people "I have life threatening respiratory problems!"

If the right diet and supplements can help resolve your hormonally based medical issues, then you have no needles, needle marks or illegal (and potentially unsafe) substances to try to hide.