In a large skillet, heat the olive oil over medium heat. Add the chorizo and cook for about 5 minutes, breaking it apart with a spatula until browned and cooked through.
Add the diced onion and bell pepper to the skillet. Sauté for another 3-4 minutes until the vegetables are softened.
In a bowl, whisk together the eggs, milk, salt, and pepper. Pour the egg mixture into the skillet with the chorizo and vegetables. Cook, stirring gently, until the eggs are just set, about 3-4 minutes.
Warm the flour tortillas in a separate skillet or microwave until pliable.
To assemble each burrito, place a portion of the chorizo and egg mixture in the center of a tortilla. Top with shredded cheddar cheese, avocado slices, and fresh cilantro.
Fold in the sides of the tortilla and roll it up tightly from the bottom to the top.
Serve immediately with salsa on the side.