Disclaimer! The advice I’m gonna give you is not from my personal experience. It’s always better to ask someone who knows more about it. I hope that if I’ll be wrong at some points blog’s followers will correct me.
Okay, thing you’re gonna need is called binding (to bind). It’s the technique that people with breasts use when they need to (or have to) hide them [breasts]. I didn’t have a personal binding experience, but I can link you to these pretty good (imo) tutorials:
That’s it. Good luck with your cosplay and be careful. :)
P.S. Dear followers (not only cosplayers!), if you had a binding experience feel free to comment under this post, reblog with facts fixes or send me an ask or fanmail. I’ll be happy to fix the mistakes or add useful stuff and links.