Jesus is referring to natural human nature, not His flesh, which is, of course, sinless, and perfect, and which exists by the divine act of being—i.e., by the same infinite act of being as the Word itself, Second Person of the Trinity.
If by “flesh” in this context, Jesus meant His own flesh, then the crucifixion and resurrection of His body would have profited the world nothing. It is precisely because HIS flesh DOES profit that He commanded us to receive it in the Eucharist. The flesh that profiteth nothing is OUR flesh.
In other words, you have ripped a few verses out of context, and indulged in the common error of assuming that a particular word, anywhere it appears in Scripture, always has precisely and exactly the same meaning.
John 6:63 It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.
That verse is included in the conversation where He is talking about HIS flesh. Trying to make a switch and infer that He somehow switched to “our flesh” is nonsense and cannot be justified in context. Those are the tactics of the RCC and why those who finally realize the RCC has been lying to them leave that organization.
>> In other words, you have ripped a few verses out of context,<<
NO, I have intentionally left the IN context as opposed to your attempt to take them out of context.
Arthur excellent depiction above. Yes Jesus Christ Truly God and Truly Man is the spotless Lamb of God who takes away the sins of the world. By His Body and His Blood our sins are washed away.
I will also note, that the Israelites when celebrating Passover ate the lamb as well. Passover was a "shadow" "type" of what was to come...The death, burial and Resurrection of Jesus Christ. One, Passover, was a physical deliverance, the second, Calvary/the Empty Tomb was spiritual deliverance.