Boyd’s Bible Dictionary:

Everything living
(Gen. 6:13-19); mankind (Gen. 6:12); the body (Col. 2:5; 1 Peter 4:6); seat of appetites (Rom. 8:1,5,9; Gal. 5:17-19; Eph. 2:3). Used much figuratively.

Concise Bible Dictionary:

This term is used in various senses in scripture. The principal are ...
1. The estate of man: "all flesh shall see the salvation of God" (Luke 3:6); "the Word became flesh" (John 1:14).
2. The material part of man and of animals: "all flesh is not the same flesh: but there is one kind of flesh of men, another flesh of beasts" (1 Cor. 15:39).
3. The same kindred: "thou art my bone and my flesh" (Gen. 29:14); "he is our brother, and our flesh" (Gen. 37:27).
4. Union: "they shall be one flesh" (Gen. 2:24; Eph. 5:29-31).
5. Man's nature, but corrupted by sin: "that which is born of the flesh is flesh" (John 3:6); "sinful flesh" (Rom. 8:3).
6. The state which characterizes man before knowing deliverance: (Rom. 7; Rom. 8:8-9).
7. Though no longer the state of the Christian, yet the flesh is in him, and is antagonistic to the Spirit, "the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other: so that ye should not do the things that ye would" (Gal. 5:17). Thus the Spirit resists in the Christian the accomplishment of the lusts of the flesh.

From Anstey’s Doctrinal Definitions:

When used with the article “the” before the word, it refers to the fallen sin-nature in man. But when it is used without the article, it usually is denoting what is human, rather than what is sinful. (Unfortunately, the KJV does not always follow this rule, as do the more critical translations produced by J. N. Darby, W. Kelly, etc.)
In keeping with this, Scripture is careful to state that the Lord Jesus came “in flesh”—leaving out the article (1 John 4:2-3; Rom. 1:3; 1 Tim. 3:16). To say, “in the flesh” in connection with the Lord’s humanity could imply that He took part in the fallen sin-nature, which He most definitely did not. However, the article “the” is rightly used in connection with men because all in Adam’s race have been born with a fallen sin-nature (Rom. 7:5, etc.).