das Fleisch
meat
The muscle tissue of animals that is used as food.
Viele Vegetarier essen aus ethischen Gründen kein Fleisch.
Many vegetarians don't eat meat for ethical reasons.

meat / flesh
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meat
The muscle tissue of animals that is used as food.
Viele Vegetarier essen aus ethischen Gründen kein Fleisch.
Many vegetarians don't eat meat for ethical reasons.

'Fleisch' (meat/flesh) is an uncountable noun (mass noun) in most of its meanings. It is therefore usually used without an article and generally has no plural.
Zum Grillen kaufen wir Würstchen und Fleisch.
For grilling, we're buying sausages and meat.
You can recognize the meaning of 'Fleisch' (meat/flesh) from context. If it is about fruit, it means the edible part. In philosophical or religious texts, it often stands for the body in contrast to the spirit.
Entfernen Sie die Kerne und schneiden Sie das Fleisch der Avocado in Würfel.
Remove the pits and cut the flesh of the avocado into cubes.
When referring to meat as food, it is often described with adjectives such as 'mager' (lean) or 'fett' (fatty), 'zart' (tender) or 'zäh' (tough), and 'roh' (raw), 'gebraten' (fried/roasted), or 'gekocht' (cooked/boiled).
Für dieses Gericht sollten Sie ein zartes Stück Rindfleisch verwenden.
For this dish, you should use a tender piece of beef.
The proverb 'Der Geist ist willig, aber das Fleisch ist schwach' (The spirit is willing, but the flesh is weak) is very well known. It describes a situation where you want to do something, but lack the physical discipline or strength.
Ich wollte heute früh aufstehen und joggen gehen, aber der Geist ist willig, aber das Fleisch ist schwach.
I wanted to get up early today and go jogging, but the spirit is willing, and the flesh is weak.
body
'der Körper' and 'das Fleisch' can both have to do with the physical part of humans or animals. 'Körper' means the whole physical human or animal body, and sometimes only the torso. 'Fleisch' mainly means muscle tissue, especially when it is meant as food. With humans, 'Fleisch' in this sense does not sound neutral and is hardly ever used in everyday language for the whole body. The words can be confused because both feel physical. For health, sports, or appearance, you say 'Körper'; for food, you usually say 'Fleisch'.

Für das Abendessen kauft Mehmet frisches Fleisch beim Metzger.
For dinner, Mehmet buys fresh meat from the butcher.
Nach dem Training braucht der Körper genug Wasser und Ruhe.
After training, the body needs enough water and rest.