Whisk lemon juice, lime juice, fish sauce, rice vinegar, sugar, cayenne, and lemon zest together in a bowl until dressing is smooth.
Spread ground turkey in a thin layer in a arge skillet; add garlic. Pour enough water into the skillet to cover the turkey; bring to a boil. Cook and stir turkey mixture, breaking the meat apart with a fork, until turkey is browned and crumbly, 7 to 10 minutes. Drain liquid and transfer turkey to a large glass bowl.
Mix red onion, carrot, chestnuts, Thai chile peppers, green onions, mint, basil, and cilantro into turkey until well combined. Refrigerate mixture until chilled, about 30 minutes.
Sprinkle rice powder and Thai chile flakes over turkey mixture and mix well.
