I'm sorry, but your word order is incorrect. Your best choice is: Have you already read this flyer?
On the other hand, my sentence is technically correct (the dictionary hint says כבר means already or yet) and makes sense but it was marked wrong. :-(
It is: Have you read the flyer yet?
The problem with your sentence is not the "yet", which is accepted, but that you said "the flyer" instead of "this flyer". You forgot to translate "הזה".