In medium bowl, break up cookie dough. Knead in flour until well blended. Shape dough into flattened round. Cover; refrigerate until firm, about 1 hour.
Heat oven to 350°F. Divide dough in half. On lightly floured surface, roll half of dough to 1/4-inch thickness. Cut with 4-inch kite-shaped cookie cutter. On ungreased cookie sheet, place cutouts 2 inches apart. Repeat with remaining half of dough.
Bake 7 to 9 minutes or until edges are lightly browned. Cool 5 minutes; remove from cookie sheet to cooling rack. Cool completely, about 15 minutes.
Spread icing over cookies. Decorate with candy sprinkles. Attach sour straws with icing for kite strings. Store loosely covered at room temperature.