Preheat oven to 350°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 4 ingredients in a large bowl. Combine egg, egg whites, almond extract, and vanilla; add to flour mixture, stirring until well blended. Stir in cherries and almonds (dough will be dry and crumbly). Turn dough out onto a lightly floured surface; knead 5 to 6 times. Divide dough in half. Shape each portion into an 8-inch-long roll. Place rolls 4 to 5 inches apart on a baking sheet coated with cooking spray; flatten each roll to 1-inch thickness.
Bake at 350° for 30 minutes. Remove rolls from baking sheet; cool 10 minutes on a wire rack. Reduce oven temperature to 325°. Cut each roll diagonally into 1/2-inch slices. Place slices, cut sides down, on baking sheets coated with cooking spray; bake 10 minutes. Turn cookies over; bake an additional 10 minutes. Remove from baking sheets, and cool completely on wire rack.