לזכות כל אהובי הכהנים שקוראים את בלוגנו!
Birkas Kohanim must be said in lashon hakodesh [sotah 35a], which indicates that the bracha is not coming from the kohanim but from the source of all kodesh - Hakadosh Baruch Hu.
A non-kohen reads out the bracha word for word and the kohanim repeat after him [Yerushalmi gitin 5/9]. This shows that the power of the kohanim to bless is derived from the non-kohanim. For every Jew has a spark of a kohen in him as it says ואתם תהיו לי ממלכת כהנים - "You should be to me a kingdom of kohanim".
That is why the kohanim don't make a bracha in the morning thanking Hashem for their special status [betcha never wondered about that!:-)]. When they thank Hashem - as we all do - that they are not gentiles that includes the fact that they are kohanim because they draw their kohanic power from the general populace of Jews.
[Mei Marom page 30 - see there for more about this]