Torah Temimah cites Toras Kohanim.
“And it shall be for the kohen like the minchah” — Scripture compares his obligatory minchah to his voluntary minchah. Just as a kohen’s voluntary minchah is not eaten (it is entirely burned), so his obligatory minchah is not eaten.
Hekesh of chovah to nedavah when the bringer is a kohen — the same “kalil” rule applies.
If the sinner is himself a kohen, the remainder of his flour-chatas is not eaten by kohanim. It is treated as a kohen’s own minchah and is burned in full (kalil). The ordinary rule that sheyarei minchah are eaten does not apply when the owner is a kohen.