In a large bowl, combine the cooked chicken, softened cream cheese, Monterey Jack cheese, red bell pepper, jalapeño, green onions, chili powder, garlic powder, smoked paprika, salt, and black pepper. Stir until evenly combined and creamy.
Divide the filling evenly among the four tortillas. Place the filling slightly below the center of each tortilla. Fold in the sides and roll tightly like a burrito.
Add about 1 inch of vegetable oil to a large skillet and heat to 350 degrees Fahrenheit.
Place the wraps seam-side down in the hot oil and fry for 2 to 3 minutes per side, turning carefully, until golden brown and crispy.
Transfer the wraps to a paper towel-lined plate to drain excess oil.
To make the avocado-lime dip, add the avocado, sour cream, lime juice, cilantro, garlic powder, and salt to a blender or food processor. Blend until smooth. Add 1 to 2 tablespoons of water, if needed, to achieve a creamy dipping consistency.
Arrange the shredded romaine lettuce and diced tomatoes on a serving platter.
Slice each wrap in half diagonally and place over the lettuce and tomatoes.
Serve immediately with the avocado-lime dip.