Put the carrots and celery in a 6- to 8-quart slow cooker. Top with the chicken; sprinkle with the garlic, red pepper flakes, ½ teaspoon salt and a few grinds of pepper. Whisk the broth with the flour in a medium bowl until smooth; pour over the chicken. Cover and cook on low, 7 hours.
About 20 minutes before serving, bring a medium pot of salted water to a boil. Add the pierogi and cook as the label directs. Drain.
Uncover the slow cooker and stir, breaking up the chicken. Add the pierogi, peas and heavy cream and stir. Let stand, uncovered, 10 minutes. Stir in the dill; season with salt and pepper.