In a large pot over medium heat, simmer chicken in 6 cups water until no longer pink. Remove chicken, cool and shred.
Return shredded chicken to pot and stir in butter, salt and pepper. Cook until chicken reaches desired tenderness, 15 to 60 minutes.
In a bowl, stir together baking mix and milk until smooth. In a separate bowl, stir together flour and 1/2 cup cold water until smooth. Stir flour mixture into soup; bring soup to a rolling boil.
Drop baking mix mixture by tablespoonfuls into the boiling water, neatly around the chicken. Reduce heat to a simmer and cook, uncovered, 10 minutes. Then cover and cook 10 minutes more. (Sneak a spatula under the dumplings to prevent chicken from sticking to the bottom of the pot.) Serve hot.