Flensburg is an independent town in the far north of the German state of Schleswig-Holstein. After Kiel and Lübeck, it is the third-largest city iā¦Flensburg is an independent town in the far north of the German state of Schleswig-Holstein. After Kiel and Lübeck, it is the third-largest city in Schleswig-Holstein. Flensburg's city centre lies about 7 km from the Danish border.