If I drink diet coke or decafinated coke when I have braces will it ruin my teeth, even if it is flat?

Yes. In conjunction with the other answer, it is also very bad to sip on a coke all day long. If you must have a soda, drink it fairly quickly. Then water to help clear the acid.
Probably YES. No matter it is non-diet or diet drink; drinking the arbonated drink will produce a temporary acidic exposure in the mouth. Especially if your own body can not produce enough buffering agent to reverse the prolonged acidic condition. To avoid and minimize this side effect, a chewing gum or drinking a cup of water after soda is recommended.