Kohen Shaliah Sssibur

I read in the kitzur shulchan aruch that a kohen should avoid being chazan during a tefillah in which birkat hakohanim must be said. Is this the halacha?

Yes-this halacha is based on a mishna in the fifth chapter of masechet brachot. Under ordinary circumstances a kohen should indeed avoid being the shaliach tzibbur.