There are two types of sesame oil. One is light in color and the other is darker because it is made with toasted sesame seeds. This recipe uses the darker sesame oil and is found in health food stores, Asian markets, or the international food section at your grocery store. Store dark sesame oil in your refrigerator, especially if you do not use it that often. My favorite brand is Spectrum and found in Health Food Stores, Trader Joes, and Whole Foods.
Chili garlic paste is found in most Asian markets and similar too Sambal Oelek. You can substitute these items with Hot Chili oil if you cannot find them. Add a little and taste as you mix the sauce, then add more as needed. If you want to keep your costs down and already have Sriracha sauce, use that instead. It has a very different flavor from the garlic chili paste but it does have a nice spicy flavor.
Black vinegar is also a specialty item found in Asian Markets. It has a very strong flavor and adds some great depth to the sauce. I totally understand if you want to skip out on buying it, but it will last forever in a cool pantry and is used in many Asian food recipes.