That only works if you have the private key for the address, which most exchanges won't give you. What exchange are you using OP?
It also requires you to give the private key to someone else, which is a bad idea.
You're not giving the private key to someone else. The code is open source and it's all client-side JS. It's probably safe, but if you want to be even more sure that the website hasn't been tampered with, you can download the script yourself and run it locally using an offline computer.
Let me rephrase that: Its unnecessarily complicated and risky to use brainwallet when signing(!) a message. Just use your client/service.