It's quite simple really; in the case of salt & pepper you have two condiments thrown together but they're still both separate while in the case of chilli salt, the salt crystals themselves are infused with the other respective ingredients. This is also why we say chicken salt because the flavour is imbued into the salt itself. Salt & chilli would bring to mind something entirely different: salt with cut/sliced chillis. In this case if you wanted to say salt & chilli you'd say something like muối và ớt (xắt).
I agree that "salt and chili" may be misinterpreted as salted chili peppers, but "peppers and salt" has the same problem, and it's more vague. It could be misinterpreted as salted chili peppers, salted bell peppers, etc.
There's no perfect translation, but I'd say "chili salt" is closest. It's not commonly said, but I think it's pretty unambiguous.