Q. If we do not believe in intermediaries, why does God bless the people by means of the kohanim?
A. The appointment of the priests to bless the people using the words laid down by God is spelled out in Numbers 6, which says, “They shall place My name on the Children of Israel, and I shall bless them”.
God can and does use any agent He chooses; why otherwise would the Bible have angels?
The Sefer HaChinuch says that in Temple times the kohanim were regarded as particularly close to the Almighty.
Another view is that the kohanim are symbolic of humankind, and God has endowed human beings with the capacity of bringing blessing upon each other.