For the mango salsa, combine all ingredients (mango through cinnamon) and stir to combine. Taste and add salt or additional vinegar, to taste. Chill for at least 1 hour before serving.
For the cucumber raita, combine all ingredients (cucumber through lemon juice) and stir to combine. Taste and adjust salt, if needed. Chill for at least 1 hour before serving.
Combine all ingredients for the burgers (chicken through pepper) in a food processor and blend until evenly combined and chicken is ground into an even, yet textured, consistency. Shape into 8 patties. Grill or cook in nonstick skillet over medium heat until cooked through, about 5 minutes on each side. Serve immediately on buns, topped with chutney and raita.