Do you mean Chef Mickey's? If so, the only direct way to get from MGM to the Contemporary on Disney transportation is via bus, which can mean waits of up to 20 minutes on each end.
Unless everything moves perfectly, and you get seated right at 6:40, you are going to be cutting it way close. Especially because you need to get to Fantasmic! well before 8:30 - it's not unusual for them to close the line off by 8:10 or 8:15, or earlier if it's busy, and unless you are there by 8 you may have to stand.
If I was going to try this, I'd use a taxi just so I'd have more control - but you'd have to hit everything perfectly to do it. Remember, a 6:40 PS doesn't mean you will be seated right at 6:40. If you are, you'd have to spend no more than a half-hour eating so you could get back to MGM in time to get in line.
If you are set on doing both the parade and Fantasmic!, I'd skip Chef Mickey's that night. You are just going to be running, running, running. I wish I could be more encouraging, but you are going from one end of the resort and it's difficult on such a tight time schedule. I'd hate for you to miss Fantasmic! because you didn't get seated until 7:15 or you missed a bus and had to wait.
Good luck in any case! Maybe you can schedule Chef Mickey's for another night?
N.E.D.