Grind the almonds. Do NOT use a food processor, as this will result in the mixture being short and unworkable. Set the oven to about 400 degrees Fahrenheit.
Mix ground almonds, confectioners' sugar and flour. Work in the egg whites in stages. The mixture must be firm, but not dry.
Roll the mixture to finger thick lengths on a icing sugar dusted board to prevent sticking, and place in ring molds or on parchment. Make sure that they are not too thick. During baking they will swell somewhat and if they are too thick, they can flow together.
If using a piping bag, choose a hole or a star which is not larger than 12 mm across. Press the ends of the length thoroughly together when making the rings, or they will open during baking. Put the molds on a baking tray, and bake in the middle of the oven for 10-12 minutes. Cool rapidly. As soon as the rings are partly cooled, tip out of molds.
For icing, mix confectioners' sugar, egg whites and vinegar to a thick mixture, and pipe this onto rings in thin line, zig-zag pattern. Pile the rings on top of another when icing is dry. The rings can be fixed together with a few drops of caramel made by melting sugar in a dry pan and lightly browning.
NOTE: Kransekake should be kept in a airtight tin. Put a fresh crust of bread or a peeled potato in the tin a couple of days before the cake is to be served. This will give it the right "chewy" texture. Can be deep frozen. You can decorate with flags, bonbons or candy.