Place chicken breasts in pot and add enough water (or chicken broth) to fully cover chicken breasts.
Bring liquid to a boil, then reduce heat and simmer until chicken is no longer pink, approximately 10 minutes.
Transfer chicken to large bowl and shred using two forks (or preferred method, see Notes).
In large skillet, heat one tablespoon avocado oil over medium-high heat. When oil is hot, add shredded chicken.
Reduce heat to medium. Stir in green chiles, fire-roasted tomatoes, and tomato sauce. Simmer 3 to 4 minutes.
Reduce heat further to simmer. Stir in taco seasoning.
Heat tortillas in microwave for approximately 15 seconds. See Notes for tips.
Remove tortillas from microwave and lay out on flat surface. Layer each tortilla with refried beans, shredded chicken mixture, and shredded cheese. Tightly roll tortillas into burritos.
Heat remaining avocado oil in large skillet. When hot, add rolled burritos seam-side down. Sear tortillas 2 to 3 minutes until golden brown, then flip and sear 2 to 3 minutes on other side.
Serve immediately with a side of guacamole (optional).