I know actual binders can be expensive. If you have a compression shirt, whether athletic or maybe one of those gynecomastia shirts from underworks (which is what I got because it is cheaper) that aren't really strong, here are two ways to fold it so that it both compresses more and does not roll undone.
1: Two layered (flattens an inch and a half to two inches depending). Turn it inside out, and hold it upside down with the back facing you. Step into it. Pull up the end without sleeves (which should be on top right now) until it covers your chest completely. Now get the sleeves and pull the rest of it up so that it layers over.
2: Three layered (flattens two inches and a half to three inches depending). Pull the shirt normally over your head and arms, but do not put it over your chest. Pull the very bottom over your chest, while leaving the rest wrinkled up at the top. Grab the wrinkled section and carefully pull out and over the other layer. You may have to adjust the innermost layer.
One good tip I found (can't remember where, would credit if I did) is to move each side of your chest outward and upward. Doing that in combination with one of the above will, for small to medium chests, give a male appearance (I have passed several times doing this).
Hope this helps!
