Preheat the oven according to the directions on the sugar cookie package. Line a baking sheet with parchment paper.
Press the sugar cookie dough evenly into a rectangle shape on the parchment to create the tart crust. Bake according to package directions, or slightly less for a softer, chewier center. The edges should be lightly golden. Cool completely before adding the filling.
In a mixing bowl, beat together the softened cream cheese, powdered sugar, vanilla extract, and lemon zest until smooth, creamy, and fluffy. Spread evenly over the completely cooled crust.
Arrange the blueberries and blackberries in the upper left corner to resemble the stars of a flag. Layer the sliced strawberries across the tart in horizontal rows to create the stripes.
Refrigerate for at least 4 hours or overnight before serving.