transportation

I only see one to Oslo, one to Goteborg, and a third to a city, not Tallinn, in Lithuania. It looks like there's a Malmo to Travemunde, Germany. You might check that out, train to the origination, I think it's near Lubeck - which isn't too far from Kiel. Then a quick train ride across the bridge to Copenhagen from Malmo (don't be surprised if this is an expensive train ticket, they need to pay for the bridge).

The most direct route between Hamburg and Copenhagen is via the Puttgarden-Rødby ferry (route E47). The direct trains also use this ferry to get to Copenhagen. There is no ferry service between Kiel and Copenhagen. Alternatively, if you are further north in Germany, you can use route E45 then E20 and the Great Belt Bridge. Are use using trains or do you drive yourself?