Whisk together the lime juice, olive oil, garlic, ground cumin, chili powder, salt, and red pepper flakes in a bowl; pour into a large resealable plastic bag.
Put the chicken breasts into the bag, coat with the marinade, squeeze out excess air, and seal the bag.
Marinate in the refrigerator for 8 hours to overnight.
Preheat the oven to 375 degrees F (190 degrees C).
Remove the chicken from the marinade and shake off excess. Discard remaining marinade. Arrange chicken breasts in a baking dish.
Bake chicken breasts in preheated oven until no longer pink in the center and the juices run clear, about 35 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Shred chicken breasts with two forks to desired texture.