Mix flour, salt and nutmeg in medium bowl. Set aside. Beat butter and sugar in large bowl with electric mixer on medium speed until light and fluffy. Add egg, vanilla extract and rum flavor; mix well. Gradually stir in flour mixture on low speed until well mixed.
Preheat oven to 325°F. Roll out dough to 1/4-inch thickness on generously floured work surface. Cut into 3x2-inch rectangles. Cut corners from one of the short ends of each rectangle so they resemble the shape of gift tags. Make a hole in between the cut sides of the cookies with a drinking straw. Place 1 inch apart on ungreased baking sheets.
Bake 8 to 10 minutes or until edges start to brown. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.
To decorate cookie tags, frost with untinted Colorful Royal Icing. Place frosted cookie tags on cooling rack to dry. Meanwhile, prepare desired colors of Flavor Paints (see Holiday Painted Cookies Recipe or Painted Sugar Cookies Recipe). Using small clean paint brushes, paint gift tag designs and messages on frosted cookie tags. Let dry.
Insert ribbon through holes of cookie tags. Place cookie tags in small clear cellophane bags leaving ribbon exposed. Carefully seal bags closed with festive twist ties or smaller pieces of ribbon. Use exposed ribbon from cookie tags to attach to ribbon on wrapped gifts.