Since a Kohen is the recipient of "Chalah" that a non-kohen separated their dough, does a Kohen have to still separate the "Chalah" portion from the dough and give it to himself?
The same question would apply to the mitzvah of "Terumah" from his / wife's fields.
Yes, everyone always has to formally declare and separate all the special portions. Any you have the right to can then be kept and used yourself.
Rambam Maaserot 1:3:
לויים וכוהנים מפרישין מעשר ראשון, כדי להפריש ממנו תרומת מעשר; וכך הכוהנים מפרישין שאר תרומות ומעשרות לעצמן. ולפי שהכוהנים נוטלין מן הכול, יכול יאכלו פירותיהן בטבלן--תלמוד לומר "כן תרימו גם אתם" (במדבר יח,כח): מפי השמועה למדו--"אתם", אלו הלויים; "גם אתם", לרבות הכוהנים.
Levites and priests [who happen to own farm products] set apart the first tithe so as to remove from it the priest's share of the tithe. So too, the priests set apart other terumoth and tithes for their own use, since they only receive from all [and are not required to give away anything to other priests]. One might think that they are allowed to eat their farm products untithed, but the Torah explicitly declares: "Thus shall you too set aside a gift" (28). Traditionally interpreted, you refers to the Levites; you too includes the priests as well.
