Heat oven to 350°F. In large bowl, break up cookie dough; stir in flour until well mixed. In medium bowl, place half of the dough; add desired amount of green food coloring, working it into dough until well blended, Wrap dough in plastic wrap; freeze 10 minutes. In separate medium bowl, place remaining dough; add desired amount of red food coloring, working it into dough until well blended. Wrap dough in plastic wrap; freeze 10 minutes.
For each color, shape dough into 12 (1-inch) balls. On work surface, roll each ball into 5-inch rope, using hands. For each cookie, overlap ends of 1 green rope and 1 red rope 1/4 inch. Working counterclockwise, wrap ropes around overlapped ends, creating a circle shape with a spiral pattern (see photo); gently press outside ends of ropes into dough for a smooth edge.
Gently pick up circles using hands and place 2 inches apart on ungreased cookie sheets. For each circle, carefully lift up edge to slide craft stick about 1 1/2 inches under circle, overlapping sticks as necessary. Decorate circles with sprinkles.
Bake 10 to 12 minutes or until edges are light golden brown. Cool 3 minutes; carefully remove from cookie sheets to cooling racks. Store in airtight container or large resealable food-storage plastic bag.