Preheat the oven to 350°F and set an oven rack in the middle position. Butter and flour, or use nonstick cooking spray with flour, such as Baker's Joy, a 9x13-inch ceramic baking pan, or metal pan. Sift together the flour and baking powder to remove any lumps in a large bowl. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, combine the unsalted butter, sugars, oil, pure vanilla, clear vanilla, and salt. On medium speed, beat until light and fluffy for about 5 minutes, stop and scrape the bowl, and paddle with a rubber spatula as necessary.

Add the eggs, beat on medium speed until well combined, about 2 to 3 minutes, and scrape the bowl. On low speed, stream in half of the buttermilk. Increase speed to medium-high and mix for about 1 minute. Scrape the bowl. Add half of the flour mixture and mix on low speed just until combined.

Scrape the bowl again, add the remaining flour mixture and remaining buttermilk and mix just until the batter comes together, about 45 seconds to 1 minute. Finish folding the ingredients by hand using a rubber spatula to ensure the batter is well mixed and smooth; there should be no streaks of fat or liquid.

Evenly pour batter into the prepared pan. Bake the Cake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean. Remove the cake from the oven and let it cool in the pan on a wire rack until completely cool.

Sift the powdered sugar and powdered milk in a large bowl to remove any lumps. Set aside.

Gradually add 2 cups of the confectioners' sugar mixture, mixing at low speed to combine. Once the confectioners' sugar mixture is mixed in, increase the speed to medium-high and beat until light and creamy, about 2 to 3 minutes; adding 1 tablespoon of milk if needed for desired consistency.

When the Cake is completely cool, spread three-fourths of the frosting in an even layer on the top of the cooled cake. Arrange the blueberries in 7 rows of 7 berries each in the top left-hand corner of the cake to form the blue portion of the flag.

Next, arrange 2 rows of raspberries across the top of the cake like a red stripe, leaving about 1 inch between each row to pipe the stripes. Place the remaining frosting in a pastry bag fitted with a star tip and pipe 1 row or 2 rows of white stripes below the raspberries. Alternate rows of raspberries and frosting until the flag is completed; pipe stars between the blueberries to form the stars. Using a sharp knife, slice and serve the cake immediately, or refrigerate until ready to serve the same day.