Dressing to conceal your breasts.

[Paa_Paw]

It has been a long time since I did this, so perhaps it is time to do it again.
The most obvious thing is a compression shirt.  Years ago I simply wore a tee shirt that was overly tight and it did the same thing but the tees would stretch out and not be good for long.  Some guys swear by the compression shirts and others swear at them and find that they are very uncomfortable.  I am in the latter group.
So anyway, a snug tee under shirt is helpful. but what goes over that is also going to make really big difference.
Avoid knits. and pull overs.  Instead use a woven fabric shirt the buttons up.  Vertical patterns and plaids are great but any pattern is better than a solid color.   Breast pockets help, but only if they are kept empty.  Dark or saturated colors seem to be better than light colors.  A shirt worn untucked will hang straight and conceal the shape better than a shirt that is tucked in.  Go up a size,  If a Large is a good fit, the XL will drape and conceal better.  But only go up one size, too loose looks sloppy. 
Some guys slouch in an attempt to hide their breasts.   It does not really work and it looks sloppy. 
If you have a trick that works well for you, please share it.

[Seanodonovan]

Here in the UK where the weather is more amenable to such clothing a loose-fit formal jacket does a lot to convert "big breast" into "big chest".  Dark colours are always better than light at disguising shape.  
Patterns can be treacherous and "draw the eye" just to where you do not want it drawn.
When I was young and doing training in our Volunteer Reserve Army I was returning from a run, wearing a white t-shirt with our Regimental badge emblazoned across the front.  The badge consisted primarily of a Maltese Cross with the sundry battle-honours of the Regiment printed on each arm of the cross.  Some honours related to the Peninsula War where Sir Arthur Wellesley (as he then was) faced the French led in the main by Marshal Soult leading to a comment from an erudite officer looking on that:
"I see you are having a Soult moment...he looked a right t*t at Salamanca too!"  (Salamanca being a battle-honour very inconveniently situated !)

[Paa_Paw]

Many years ago, when I reached the point in the Police academy when we received our Badges, The old police captain pinned my badge on then commented in his accented speech: " Now, 'eres a lad wot wears 'is Badge proudly."  I too had to laugh.