Put the chicken breasts in a small pot and cover with 1-inch of water. Bring to a boil, then reduce heat to a simmer. Cook until an instant-read thermometer reads 165 in the center of the thickest part. About 10-15 minutes. Remove from water and shred well with forks.
Salsa de Aguacate
Put the serranos, tomatillos, and garlic cloves in a small pot and bring to a simmer. Cook for 15 minutes. Drain.
Remove the stems from the serranos, then slice them in half longways and scrape out the seeds and white veins (if you want it hot, leave in the seeds and veins). Peel the garlic. Add all of the salsa ingredients to a blender jar and blend until smooth.
Heat 1 tbsp. cooking oil in a nonstick pan over medium-high heat. Add the onion and saute until beginning to turn translucent. About 3 minutes. Add the garlic and saute an additional 30 seconds. Add the chicken, diced tomato, salt, and pepper. Saute for an additional 2 minutes and set aside to cool for about 5 minutes.
In a medium-sized bowl, add the chicken mixture and all of the shredded cheese.
Wrap the tortillas in a paper towel and microwave for one minute, until soft.
Add about 3 tablespoons of the chicken mixture to two tortillas, then roll each one tightly and pin them together with two toothpicks. Be certain that the flaps on the tortillas are pinned down so they don't come open when frying.Continue stuffing, wrapping, and pinning your tortillas until you have six bundles of two tortillas each pinned together.
Heat the vegetable oil in your dutch oven until it reaches 350 degrees. Fry two bundles of flautas at a time, 1-1/2 minutes on each side. Remove them to a paper towel-lined plate. As you lift the flautas out of the frying oil, tilt them to the side so any oil inside will pour back out into the pot.Continue frying two bundles at a time until everything is done.
Remove the toothpicks, top with the salsa de aguacate, and any additional garnishes you choose. Serve immediately.