Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment paper.

Combine shredded chicken with salsa, cumin, and oregano in a large bowl.

Prepare Spanish rice according to package directions. Remove from the heat.

Stir rice and shredded cheese into chicken mixture. Divide mixture among flour tortillas; wrap and place seam-side down on a lined baking sheet. Brush with oil.

Bake in preheated oven until golden brown and crispy, about 20 minutes. Serve, if desired, with your favorite toppings.