Combine oat flour, potato starch, cornstarch, tapioca flour, xanthan gum, yeast, sugar, and salt in the bowl of a stand mixer; whisk until well mixed, about 1 minute.
Whisk milk, egg, olive oil, and vinegar together in a separate bowl until well combined, about 1 minute. Stir milk mixture in gradually to the flour mixture on low speed; mix until a soft dough comes together, about 5 minutes.
Line 2 baking sheets with parchment paper. Divide dough into 6 equal pieces; roll each piece on a floured surface to a 6-inch circle. Place on the prepared baking sheets; cover with plastic wrap and set aside for 1 to 1 1/2 hours.
Preheat the oven to 450 degrees F (230 degrees C). Heat a pizza stone in the oven.
Spray pita breads with water and place them straight on the hot pizza stone.
Bake in the preheated oven until puffed and lightly golden, 5 to 7 minutes.