Melt butter in a large skillet over medium heat; cook and stir green chiles and tomato in the melted butter until tomato is softened, about 5 minutes. Crack eggs directly into the skillet and stir until yolks break; cook until eggs are scrambled and slightly set, 2 to 3 minutes.
Sprinkle tortilla chips over eggs; mix chips into eggs. Move egg mixture to the side of the skillet, turn off heat, and sprinkle egg mixture with Cheddar cheese. Cover skillet and set aside until cheese is melted and eggs are cooked through, about 5 minutes.
Stack flour tortillas on a microwave-safe plate; microwave until tortillas are warmed, about 30 seconds.
Spoon egg mixture onto each tortilla and top with about 1 tablespoon taco sauce.
