Place chicken thighs in a medium saucepan and add just enough water to cover completely. Bring to a simmer and cook for 20 minutes, or until cooked through. Remove chicken and allow to cool slightly, reserving cooking liquid.
Combine soy sauce, ginger, pepper flakes, and green onion in a small jar, shake well and set aside.
Cut chicken into chunks and place in bowl of food processor. Add mushrooms, onion, hoisin, mustard, and sriracha. Process until ground and well combined.
Beat egg with the 1 tsp water. Working in small batches, place 1 tbsp of meat mixture on center of each wonton wrapper. Brush two edges with egg wash and fold up sides, corner to corner, to seal well around filling. Fold top corner over and secure with a little more egg wash if desired.
Bring reserved cooking liquid to simmer in a pan with a steamer basket. Spray basket with cooking spray and place dumplings in basket.
Cover with lid and steam 8-10 minutes.
If you would rather cook these like potstickers with a crispy bottom, spray a shallow pan with cooking spray and set over medium heat. Set dumplings directly in pan and pour hot cooking liquid around dumplings to about 1/2 inch deep. Cover and cook 5-6 minutes or until bottoms are brown and crispy. Don't move them around during cooking or they will stick and tear.
Serve with sauce.