Heat a dry skillet over medium heat. Add the Szechuan peppercorns and dried chili flakes. Toast them for a minute or two until fragrant, stirring frequently to prevent burning. Transfer the toasted spices to a mortar and pestle or a spice grinder, and grind them into a fine powder.
In the same skillet, heat the vegetable oil over medium-high heat. Add the minced garlic and grated ginger. Stir-fry for about 30 seconds until fragrant.
Add the ground Szechuan peppercorn and chili flake mixture to the skillet, stirring continuously for another 30 seconds to release their flavors.
Add the sliced bell peppers and stir-fry for a couple of minutes until they begin to soften.
In a small bowl, whisk together the hoisin sauce, soy sauce, rice vinegar, and sugar. Pour this sauce into the skillet and stir well to combine all the ingredients.
Reduce the heat to medium-low and let the sauce simmer for a few minutes until it thickens slightly. Taste the sauce and adjust the seasoning with salt if necessary. Remember, Szechuan chicken is meant to be spicy, so don't hold back on the heat!