鳥 means bird or poultry. It's understandable that 鳥肉 would be chicken meat since chicken is the most popular "bird meat".
But in this case where chicken has monopolized the meaning of bird, how would you express duck meat?
With the kanji for duck, of course!
Though 鴨 is more commonly written in kana as かも or カモ.
Chicken meat is "tori niku" (鶏肉) and duck meat is "kamo niku" (鴨肉).