In a small saucepan, combine the first seven ingredients; add enough water just to cover. Bring to a boil. Reduce heat. Cover and simmer for 55 minutes or until meat is tender.
Meanwhile, in a small nonstick skillet, saute tomatillos and onion in oil until tender. Remove from the heat; stir in the chillies, cilantro, garlic, salt and pepper. Cool slightly. Process in a food processor or blender until pureed. transfer to a small bowl; cover and refrigerate until serving.
Remove meat from saucepan. Strain liquid, reserving onion mixture. When meat is cool enough to handle, shred with two forks. Combine onion mixture and meat; divide between tortillas. Roll up and secure with toothpicks.
In an electric skillet or deep fat fryer, heat oil to 375. Cook flautas until golden brown, turning to cook all sides. Drain on paper towels. Serve with the salsa verde.