Rinse steak and pat dry. Cut into 4 equal pieces.
Set an 11- to 12-inch frying pan with ovenproof handle over high heat; when pan is hot, add oil and tilt to coat pan bottom. Add steak and cook, turning pieces once, until browned on both sides but still rare in the center (cut to test), 6 to 7 minutes total. Remove from heat and add tequila and vinegar to pan. Light with a match (not under an exhaust fan or any flammable materials) and shake pan until flames subside.
Lay chilies equally on steaks; top with cheese slices. Broil 4 inches from heat just until cheese is melted, 1 to 2 minutes.
Meanwhile, pit, peel, and thickly slice avocado.
Transfer steaks to plates. Spoon any pan juices around meat. Arrange avocado equally on portions. Add salt and pepper to taste.