I try to make sure I eat as much white meat from chicken as I can.
Chicken meat is chicken meat!
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
It also has the more common reading of とりにく. Remember how 鳥 is とり? Chicken meat is technically also just bird meat. You can say that too!