Could You Kindly Question Mark?

The Chicago Manual of Style (CMOS 6.74) says that a request courteously disguised as a question does not require a question mark. As examples, it gives Will the audience please rise. and Would you kindly respond by March 1. This would indicate that while using a question mark is not wrong, it may not be required.

Can we use question mark with could?

Question marks should not follow questions that are disguised requests: “Could you please close the door on your way out.” (In writing, such requests are best rendered more concisely: “Please close the door on your way out.”)

Is it correct to say could you kindly?

Both are polite, and no reasonable professor would take objection to either. If you wanted to sound a little more formal, you could say I should be most grateful if you would send me the document.