Place the oil in small pot over medium heat. Heat for 3-4 minutes, or until the oil is hot. Meanwhile, as the oil heats, place the chili flakes, sugar, salt, & garlic in a wide-mouthed jar or a small ceramic bowl. Carefully pour the hot oil over the pepper flake mixture. The oil will immediately simmer & cook the aromatics. Set aside to cool. Once cooled completely, seal & store for up to 3 weeks.
Place cubed chicken breast in a food processor. Pulse 30 seconds, or until finely chopped into coarse pieces. To a small bowl, add the cornstarch, oyster sauce, sesame oil, shaoxing wine, soy sauce, bouillon, sugar, salt, & white pepper. Mix to combine well. Pour into the food processor. Pulse 5 seconds, until blended. Set aside for 20 minutes. Add the chopped mushrooms & green onions to the food processor. Pulse 5-8 seconds, until the veggies are blended into the chicken well. Transfer to a bowl.
Line a sheet pan with parchment paper & place on a work surface alongside the filling & a small bowl of water. To wrap & fold the chicken wontons, place a rounded tsp of the chicken mixture in the center of one of the square wonton wrappers. Fold the wrapper in half to form a triangle. Bring the two end points of triangle's longest edge together, then use a finger to tap a little water on the end points & press down to seal them together. The wonton wrapper should be snuggly wrapped around the meat filling, similar to a tortellini but with delicate & fluttery edges. Repeat.
Bring a large pot of water to a boil over high heat. Once the water reaches a roaring boil, drop the wontons into the pot one by one – work in batches as needed. Cook 2 minutes, gently stirring occasionally to prevent sticking. After 2 minutes, lower the heat to medium. The wontons will begin to float to the top of the pot by the 3-minute mark – cook 1 minute longer, or 4 minutes total, until the wrappers are tender & the chicken filling is cooked through. Use a slotted spoon to transfer the cooked wontons to a serving bowl.