I've done this journey in reverse, but it was about 5 years ago and quite early morning. I used the Train from Kiel Hbf to Hamburg Hbf and then the Hamburg U-Bahn to the airport. It took around 1:45 hours if I remember correctly.
The train will involve a change which in Hamburg Hbf I think would mean coming from the underground and to the main level using steps. Could have changed a bit now though as I've not been to Hamburg since then.
If there is a bus directly from the airport to Kiel then that'd probably be the better option if carrying your luggage is a big problem.