Process chicken in food processor until finely chopped.
Remove to a medium bowl; stir in carrot, scallions, garlic, cilantro, soy sauce and red pepper flakes. For each dumpling, place about 1 rounded tablespoon of chicken mixture in center of wonton wrapper.
Dip a finger in a cup of water and run it around edges of wrapper; fold up each corner to center and press together.
Place dumplings in steamer. Cover and cook until dumplings are firm. about 10 minute.