In a large Dutch oven or heavy-bottomed pot, whisk together chicken broth, cream of chicken soup, flaky poultry seasoning, salt and black pepper until smooth. Add chicken breasts or thighs. Bring to a gentle boil, then reduce heat to a steady simmer. Cover and cook for about 25–35 minutes, or until chicken is fully cooked and tender.
Remove the chicken. Shred or cut into bite-size pieces, and set aside.
Sprinkle half of the flour on a clean surface. Place the biscuits on top. Sprinkle the remaining flour on top of the biscuits. Using a rolling pin, roll each biscuit out until thin (about ⅛–¼ inch thick).
Using a pizza cutter or knife, cut the biscuits into strips, then cut across to form squares or rectangles. Shake off the excess flour.
Drop the floured dumplings into the pot one at a time, lightly scattering them to prevent sticking. Once all dumplings are added gently press them down into the broth so they’re moistened.
Return the cooked chicken. Do not aggressively stir. Simmer on low for 15–20 minutes. After 15 minutes, gently stir to prevent sticking and continue cooking uncovered another 5–10 minutes, or until dumplings are cooked through and tender.
Taste and adjust seasoning if needed. If thicker than desired, add a splash of chicken broth or water to desired texture. If a thicker texture is desired, add a mixture of equal parts water and cornstarch (1-2 tablespoons each). Serve hot.