For certain high-intensity flavours, often people use extracts (think stuff like "vanilla extract") or essential oils (i.e., oils that are the "essence" (or are infused with same) of a given plant or something). This allows you to use a very small amount of the flavouring substance in something like coffee or confectionery or so.
However, certain extracts or might just be artificial themselves, and give you that same "off" after-taste. This might be what's in your bag of beans/grounds and why you're in this predicament in the first place. The ingredient label might have some hints but is probably not helpful ("natural and/or artificial flavourings" perhaps). Here's one (judgemental) example of how the ubiquitous hazlenut flavoured coffee (from Serious Eats) could be made.
For butterscotch that you cite, for example, you could use something like butterscotch extract (example from Amazon). You could also use some other caramel or butterscotch syrup, or even make your own.
For particular flavours, after you've identified them, you might ask over at Seasoned Advice. But I'm glad you asked here first :)