Heat the olive oil and butter in a large skillet over medium-high heat. Add the hash browns. Cook, stirring occasionally, until the hash browns have browned, about 8-10 minutes.
Meanwhile, in a separate pan, cook chorizo until browned and crumbly; drain excess grease.
In a large bowl, lightly whisk the eggs. Whisk in the taco seasoning. When the hash browns have browned, push them to one side and add the eggs into the skillet. Cook, stirring frequently, until the eggs have set. Stir in cooked chorizo, green chiles, cheese and cilantro.
Warm the tortillas. Place 1/8 of the egg mixture down the center of each tortilla. Roll up like a burrito and wrap tightly in heavy duty foil. Store in a Ziploc bag in the refrigerator or cooler until ready to serve.
When ready to cook, place wrapped burritos in hot coals next to fire. Let the burritos sit in the coals, turning once, until heated through, about 10-15 minutes. (The time will depend on how hot your fire is.) Or cook on an outdoor grill.