Frozen Pina Colada Pie

This is one of my own creations as I love coconut macaroons and it goes over great in summer!

1 1/3 cups sweetened coconut flakes
1/2 cup granulated sugar
2 tablespoons all-purpose flour
1/8 teaspoon salt
2 egg whites
1/2 teaspoon vanilla extract
3 cups vanilla ice cream
3 tablespoons rum
5 ounces frozen pi