Whisk sea salt, black pepper, cumin, paprika, Italian seasoning, and garlic powder together in a bowl. Season chicken breasts with seasoning mixture and place chicken in the slow cooker.
Stir cream of mushroom soup, Italian dressing, sour cream, Parmesan cheese, flour, and vinegar together in a bowl; pour over chicken.
Cook on Low for 6 hours.
Shred chicken in the slow cooker using 2 forks.
Bring a large pot of lightly salted water to a boil. Cook angel hair in the boiling water, stirring occasionally until cooked through but firm to the bite, 4 to 5 minutes. Drain.
