Not the physical body
The body is not bad, nor does it tempt us to sin. These tendencies are from the soul residing in the spiritual realm and tangled up with the spirits of darkness and wickedness. Confusion in this by Christians has its roots in the blending of Christianity with Greek philosophy from the earliest of days.
The word "flesh" in the New Testament has various meanings. It is common for a New Testament writer to use several different meanings of a word in the same book or letter, and even in the same passage.
Sometimes people create doctrines by mixing up these meanings.
The various meanings of the word "flesh"...
The phrase "flesh and blood" refers to people, not to the physical body.
Paul didn't go to the apostles or to anyone else to confirm that his revelation from Christ was real and true.
The souls and spirits of a married couple become intertwined. I don't believe this is referring to conjugal relations as it is often interpreted — Jesus seems to be talking about something more profound. This seems to refer to a continual state, not an occasional act.
For we are members of his body, of his flesh, and of his bones. For this cause shall a man leave his father and mother, and shall be joined unto his wife, and they two shall be one flesh. (Ephesians 5:30,31)
In receiving salvation through faith in Christ, we become part of the family of God. Our souls become spiritually united with Jesus in a similar manner as occurs with a married couple. I don't believe this is referring to conjugal relations as it is often interpreted — Jesus seems to be talking about something more profound. This seems to refer to a continual state, not an occasional act.
But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God. (John 1:12,13)
This verse refers to spiritual rebirth of a believer. This spiritual rebirth is not like human birth nor is it something we can provide for on our own (3 examples)...
The part of the soul more easily influenced by sin
One part of the soul (the spirit) is strong, the other (the flesh) is weak. I don't believe the flesh referred to here is the body. It is not the physical world that tempts people to sin but it is, rather, the spiritual realm.
I speak after the manner of men because of the infirmity of your flesh: for as ye have yielded your members servants to uncleanness and to iniquity unto iniquity; even so now yield your members servants to righteousness unto holiness. (Romans 6:19)
The word "members" refers to every part of the body which can express sin including: vocal chords (sinful speech), face (hateful grimaces), hands and arms, etc. But the sinful expressions of people originate within their soul and attitude so the physical members of the body are merely expressions of the soul of humans.
For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God? (Hebrews 9:13)
The purpose of the Old Testament animal sacrifices was to cleanse from sin. It is not the body which is stained by sin but the soul, specifically, the sin nature.
The part of the soul that sins
Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness [lust], idolatry, witchcraft, hatred, variance [conflict], emulations [rivalries], wrath, strife, seditions [rebellions], heresies, envyings, murders, drunkenness, revellings [noisy parties], and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God. (Galatians 5:19-21)
This verse makes it clear what the flesh is. It is not the body
These works of the flesh each have a mental and a physical component. The important point is that it is not the body which causes these, it is the depraved soul. Therefore, the word "flesh" does not mean "body". It refers to that part of the soul which entices us to commit sin and which drives us to sin.
In this verse the word "flesh" clearly does not refer to the body, it refers to that aspect of our soul and will which is influenced by sin and which performs sinful behaviors.
Paul uses the word "crucify" to mean kill. Notice that it is not the body which is killed upon redemption but, rather, the sin nature which resides in the soul and which causes sinful actions and attitudes.
Humans have ancestors and descendants.
The word "flesh" refers to ancestors and descendants.
Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire. (Jude 7)
The phrase "strange flesh" refers to promiscuous homosexual relationships.
Paul is referring to the Jews.
Paul goes on to recite his pedigree as well as his religious achievements as a Jew.
Jesus is telling them that he is not merely a phantom, an apparition, but that he is fully present in the physical realm, that he has a body.
Paul is not in Colossae with them but is thinking about them from somewhere else. The phrase "in the flesh" means "in person".
Paul is referring to food sacrificed to idols.
We take care of our physical bodies. Just as we look after our physical body, Jesus looks after the church.
The physical aspects of life
There are two aspects to life: the physical (in the flesh) and the spiritual (in the Lord.) Paul was asking Philemon to consider his slave Onesimus to be his equal in the physical realm, that is, to free him as his slave. He was also asking Philemon to consider Onesimus to be a brother in the Lord.
Jesus is referring to his literal body, but not to his physical body. In the spiritual realm Jesus manifests his human nature in various forms...
This is a citation from Psalms 16:9. The word "flesh" refers to the person after death, clearly not the physical body which decays, but to the person who lives on after death. It seems to me that the spiritual body animated by the soul is referred to rather than the soul itself.
Human nature, physical plus spiritual, body and soul
Jesus was fully human with a human body and soul. He was also fully divine. The word "flesh" in this verse refers to full humanity in all its aspects. In taking on human nature (the flesh) Jesus "deified" human nature making it possible for us humans to become deified as well. This occurs at the final resurrection just before the Great White Throne judgment. Once deified we are not God nor gods but we will have the same nature that the human side of Jesus had (and still has).
Jesus took on full human nature. This includes body and soul.
And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory. (1 Timothy 3:16)
Jesus took on full human nature. This includes body and soul.
Works as opposed to faith
Every aspect of salvation is by the spirit, not of the flesh. The word "flesh" in this verse refers to the activities of people who are trying to perfect themselves in faith through emphasis on works, by working, by doing devotions and prayers and ceremonies
Note that this use of the word "flesh" refers to the soul and the spiritual realm — it is not the body which attempts to perfect itself spiritually but, rather, the soul. Some commentators I've read seem to limit the word "flesh" to the physical body but this is incorrect. Some uses of the term do mean this but many do not as I have shown.
The word "flesh" refers to Abraham's attempt to fulfill God's promise by having a child with Sarah's maid. He was not acting in faith.
The pus which exudes from diseased skin
The image of a garment spotted by the flesh refers to the Old Testment Levitical law of ceremonial uncleanness. The example in Jude is of a person with a skin condition which stains the clothing rendering both the person and the garment unclean. The garment must be burned and the person quarantined until the condition heals.
When a man shall have in the skin of his flesh a rising, a scab, or bright spot, and it be in the skin of his flesh like the plague of leprosy; then he shall be brought unto Aaron the priest, or unto one of his sons the priests. (Leviticus 13:2)
He shall therefore burn that garment, whether warp or woof, in woollen or in linen, or any thing of skin, wherein the plague is: for it is a fretting leprosy; it shall be burnt in the fire. (Leviticus 13:52)
This meaning of the image of flesh in this verse is that we should avoid people who teach error and should rescue innocent people who are deceived by their lies.
Flesh and bones vs flesh and blood
Jesus uses the phrase "flesh and bones" which seems to have all the same meanings as the word "flesh" as the following passages make clear.
Some make a strong distinction between the phrases "flesh and bone" and "flesh and blood" but I doubt such a distinction exists (except when referring to literal blood or literal bones). It seems that when the word "blood" or "bone" is associated with the word "flesh" it means the same as when the word "flesh" is used alone.