This mitzvah and the previous one are a pair. Just like oil (a) was an added expense for the poor person who brought a flour sin offering and (b) would raise the prestige of a sin offering, counter to its intended message, so, too, frankincense.
The Rambam refers us to the Mishna (Menachos 5:4), that if one put both oil and frankincense on a flour sin offering, he would be liable for each one individually. From this, it is apparent that they are two separate mitzvos.
As with the previous mitzvah, this prohibition applies to male kohanim in Temple times. It is likewise discussed in various places in the Talmudic tractate of Menachos, most heavily on pages 59a-60b. It is codified in the Mishneh Torah in the twelfth chapter of Hilchos Maaseh HaKarbanos and is #103 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.