Is the income of a person who works in a shop in America selling coffee, juices, sweets, and chicken slaughtered in a non-Shar'i (unlawful) manner considered permissible?

Selling permissible items such as coffee, juices, and sweets is lawful (halal), and their price is lawful. As for selling forbidden items, such as carrion—which includes unslaughtered (non-dhabiha) chicken—it is unlawful (haram). It is not permissible to eat it or sell it, even to non-Muslims, for the jurisprudential rule is: "What is forbidden to take is forbidden to give, gift, and sell." Allah Almighty has forbidden carrion. Whoever sells both permissible and forbidden items has wealth mixed between lawful and unlawful.