Preheat your oven to 400 degrees fahrenheit and line a baking sheet with parchment paper.
Roll out the gluten free flaky pie crust dough between two pieces of parchment paper into a large rectangle about 1/8 inch thick. Cut the dough into 8 equal-sized rectangles.
In a small bowl, stir together the strawberry jam and cornstarch to thicken the filling.
Spoon 1 tablespoon of the jam mixture into the center of 4 rectangles. Place the remaining 4 rectangles on top and use a fork to crimp and tightly seal the edges.
Place the pastries on the baking sheet and poke a few small holes in the top of each to vent steam. Bake for 15 to 18 minutes until golden.
While they cool, whisk the powdered sugar, milk, and vanilla extract until smooth. Spread over the cooled pastries and top with rainbow sprinkles.