Using a mixer, cream butter, shortening, oil and sugar in a large bowl until fluffy and creamy. Add egg, honey and almond extract; beat until smooth. Add oats and flour; knead until a soft dough forms. Cover and refrigerate 1 hour.
Preheat oven to 350 degrees. Grease 2 cookie sheets.
On a lightly floured surface, roll dough to 1/2-inch thickness. Cut 3 inch heart shapes and 1 inch star shapes with floured cookie cutters, in equal numbers. Transfer to prepared sheets. Bake in prepared oven for 10-12 minutes or until light brown. Transfer to a wire rack to cool completely.
For icing, combine sugar and milk in a large bowl; beat until smooth. Transfer a scant 1/2 cup white icing to another small bowl; tint blue and cover. Transfer 1/4 cup white icing to another small bowl; add water and stir until smooth. Tint red and cover.
Cover remaining icing to keep soft. Ice star-shaped cookies blue and heart-shaped cookies white. Allow icing to harden. Use a small round paintbrush and red icing to paint wavy lines on heart-shaped cookies to represent the stripes on our flag. Allow icing to harden. Place a small drop of icing to the point of the heart and place one star shaped cookie on it. Press lightly to set. Allow all iced cookies to set. Store in an airtight container. Makes 3 1/2 dozen cookies. Enjoy!