So 肉｛にく｝ refers to meat in general. It is typically used with an animal to form a particular kind of meat:
- 牛肉｛ぎゅうにく｝: Beef
- 豚肉｛ぶたにく｝: Pork
- 鶏肉｛とりにく｝: Chicken
It can also be used to describe the appearance/cut, for example in 挽｛ひ｝き肉｛にく｝, minced meat.
You talk about
- カツ: This word does not describe pork meat in general but rather a particular cut of pork meat, a cutlet (カツレツ). 丼｛どんぶり｝ itself means "rice bowl", meaning that カツ丼{どん} is a bowl of rice topped with a cutlet. 豚丼｛ぶたどん｝ also exists, but it is another dish.
- チキン: Obviously comes from the english chicken, but it never used to refer to "chicken meat" in general nor to refer to the animal. You will find it in many compounds though. These are mostly dishes names, imported or not, such as チキンナゲット、チキン南蛮、チキンカツ、ローストチキン... Many dishes also use 鳥、such as 焼き鳥. Finally, most "kinds" of chicken meat use 鳥/鶏: 鶏もも肉、若鶏、鶏胸肉
To answer your question, 肉 means meat in general. The other words you quoted have a more restricted meaning.
You can find 肉 by itself in 肉まん, which is a kind of steamed bun containing pork meat. The meat of 肉 is also found in 肉食｛にくしょく｝, meaning carnivorous, that is not related at all to beef in particular. 肉 can even have more abstract meanings in other compounds, look on goo.ne.jp or jisho.org for examples.
Good luck in your studies !
