I found the following definition in the Catechism.
"The term “flesh” refers to man in his state of weakness and mortality." (CCC 990)
Are there any other sources that deal at length with this topic?
The clear meanings can be easily gleaned from the Sacred Scripture:
John 1:14 And the Word became
flesh, and dwelt among us (and we beheld his glory, glory as of the only begotten from the Father), full of grace and truth.
Matt 19:5
For this cause shall a man leave his father and mother, and shall cleave to his wife; and the twain shall become one
flesh?
Mark 13:20
And except the Lord had shortened the days, no
flesh would have been saved: but for the elect’s sake, whom he chose, he shortened the days.
Luke 29:39
See my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not
flesh and bones, as ye behold me having.
John 6:51
I am the living bread which came down out of heaven: if any man eat of this bread, he shall live for ever: yea and the bread which I will give is my
flesh, for the life of the world.
John 6:52-56 The Jews therefore strove one with another, saying, How can this man give us his
flesh to eat?
Jesus therefore said unto them,
Verily, verily, I say unto you, Except ye eat the flesh of the Son of man and drink his blood, ye have not life in you.
He that eateth my flesh and drinketh my blood hath eternal life; and I will raise him up at the last day.
For my
flesh is meat indeed, and my blood is drink indeed.
He that eateth my
flesh and drinketh my blood abideth in me, and I in him.
There is no confusion whatsoever except for one that chooses not to understand and not to believe.