Heat oven to 350°F. In large bowl, break up cookie dough. Stir or knead in flour and food color until blended and color is even. Remove half the dough, and refrigerate remaining dough until needed.
Shape dough into 12 (1 1/4-inch) balls; roll in red sugar and place 2 inches apart on ungreased cookie sheets. With thin sharp knife dipped into flour, cut each ball into 6 wedges, cutting 3/4 of the way down into ball but not through bottom. Spread wedges apart very slightly to form flower petals (cookies will separate and flatten as they bake). Repeat with remaining dough and red sugar.
Bake 10 to 12 minutes or until set and edges just begin to brown. Immediately press 1 gumdrop in center of each cookie. Cool 1 minute; carefully remove from cookie sheets to cooling racks. Cool completely, about 10 minutes. Store in tightly covered container.