This is a very specific niche question, which is not necessarily bad but makes a satisfying answer more unlikely. I can't answer your question directly as I know close to nothing about currency issues, but I might be able to provide some context.

Kiel was part of the Duchy of Holstein which in turn was part of the Holy Roman Empire of German Nation (a multi-ethnic, political entity of early Medieval origin which doesn't confer to modern conceptions of nationhood and state). The Duke of Holstein however was the King of Denmark since the late Middle Ages (if I remember correctly). While this might seem as an obvious conflict of interests to a modern observer, it was not unique. As the Napoleonic Wars finally ended the Holy Roman Empire in 1806 and the map of "Germany" was re-drawn, Holstein did become an actual, official part of Denmark for a short amount of time. (At least until the Vienna Congress in 1815, I'm on my phone, so I fear that it doesn't become more precise right now.)

But Holstein did also become a member of the new German Confederation after Vienna and the Danish-German conflict over Schleswig and Holstein lead to two wars (called the Schleswig Wars in English) over the course of the 19th century, which ultimately ended with Schleswig-Holstein becoming a part of modern Germany (to this day).

Well, long story short, at the beginning of the 19th century, the city of Kiel was to become officially Danish, what it practically had been already for quite some time. With this in mind, Danish coins most certainly were commonly used and probably close to a currency as it gets.