The correct answer should be that you need to provide the information required to identify your account at Turkish. So if you think about it, is the information you provided enough to identify your account at the desired FF-program? You should also know the answer to your question.

If the form requires you to select an airline/FF-program, the airline/FF-program -specific account prefix (TK in this case) is implicit, and you should not specify it again. If you specify it again, the id you give would end up as TKTK<your number>, which is not what you want and may or may not need to be manually corrected by someone, possibly after you complain about missing miles/status.

If the form does not require you to select an airline/FF-program, you obviously need to provide the TK-prefix, as otherwise no one will know what airline /FF-program <your number> belongs to.