Heat a slow cooker on Low. Add hot sauce, cream cheese, and blue cheese dressing; mix until combined. Add chicken breasts; cook until fork-tender and no longer pink in the center, at least 4 hours. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Preheat oven to 350 degrees F (175 degrees C).
Pull chicken meat apart with a fork; stir into the sauce. Transfer chicken mixture to a baking pan. Top with Cheddar cheese and blue cheese.
Bake in the preheated oven until top is golden brown and bubbly, about 15 minutes.