I haven't worn a binder on an airplane (yet), though I don't see why it would be a problem. It might be a bad idea for long flights because I've heard it's a bad idea to wear a binder for extended periods of time (over 8 hours), but it should be fine for a three-hour flight.
You'd have no problem getting a binder through security. They'd only question anything that looks suspicious. As long as you don't have any weapons or explosives in your suitcase, you should get through just fine. I'm sure I've brought harmless stuff through that probably looks more suspicious than a chest binder. One time when I flew, I forgot to take out my e-cig (which looks nothing like a real cigarette) and e-liquid bottles from my backpack when I went through security (here in the US, you have to take any liquids out of your carry-on luggage when you go through security). They didn't question me about the strange device and small bottles of liquid in a pocket in my backpack. I didn't even realize I'd forgotten to show them until after I got through security! So, yeah, if something like that can go through security without raising suspicion (even though I technically violated TSA rules by keeping it in my backpack), a chest binder definitely won't cause any issues.