Looking for real/first hand help (i.e. not theoretical)  on what has worked for you.  More layers isn't a great option in the summer [emoji6].

So far sports bras are the only real option,  but they can be pretty obvious,  especially with a little perspiration.

Clara

I found wearing something like a tight fitting singlet/camisole/sports top under a loose shirt usually worked best for me, even in warmer weather. Depends on how much development you're trying to hide of course. There's a certain point where they will be noticed regardless. I recommend against binding - you don't want to do that to developing breasts.

Thanks grace.   Agree with you on the binding.

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I use a shaper camisole to keep the girls in check. It looks no different then a Tee shirt under anything else and does a far job flattening them. BTW a B cup

Sports bras are not so great when you go beyond B cup.  At least that was my experience.  You get the uniboob look which jumps out. 
I encourage racerback front close bras and two shirt layers.  T-shirt and button up is the way to go.  It may be summer and it may be impractical to wear layers but, welcome to the gonnabe girl club.  We have to pay a bit of a price before we jump out of the closet.  Thank heavens for air conditioning. 

If you really really can't go with multiple layers and are B cup or less then you might be able to get away with a thick oversized t-shirt.  In my case I normally would wear a Large but for that purpose I go with X-Large.  Large is slightly baggy already.  X-Large with thicker fabric masks a number of curves, or used to.  There is a limit after all.

Good luck.

I used to wear sleeveless white "beater" shirts under my baggy button down shirts and the combination of the two kept things hidden until I came out.

Take some tips from the ftm side Patterned shirts break up the lines of your cheat, slightly baggy helps to, anything like plaid our Hawaiian shirts, for more formal occasions a vest and or a shirt with two breast pockets, throw a pen or something into one pocket and even if someone see something they will often assume outs just something in the pocket.

Also posture hunched shoulders and leaning posture make things less clear.

I actually was concerned about this a few months ago at 4am I even googled binders Google showed me a bunch out office supplies which made me Remember the whole world is not trans :-)
It was the next day I decided how I would deal with it off my chest got too visible before I was ready to transition. I decided to do nothing if someone asked why I had breast I figured I would just say "there nice right" or something similar. Then again when people would ask me if I am gay I would just smile and say "that's more complicated than you realize.

Then I solved that problem when I went full time 6 months ahead off schedule.

Serena

When occasionally I'm on the male side of the spectrum and need to hide my chest (like traveling to Russia lol) I have a few compression undershirts that work fine. Lots of men have gynecomastia (google that to find undershirts), so it isn't a thing to wear one under a shirt. Yeh, they're hot in the summer, but again, if you have to, you have to. Spanx actually makes a few types, though mine are older and a different brand whose name I cannot recall.... UNDERWORKS! That's the one.

Tight cotton tee shirt, under whatever even in Summer... (B cup too) and has worked for many years, is comfortable and evens the shape and holds the bouncies in check (to a degree) 

Katy xx