John 6:63 It is the Spirit who gives life; the flesh is no help at all. The words that I have spoken to you are spirit and life.
It's the SPIRIT who gives life. Not eating.
The flesh, that He just talked about, is NO HELP AT ALL. IOW, it doesn't do anything. He's telling us that He's speaking a SPIRITUAL truth, not a physical one.
Jesus did not say, "My flesh is of no avail." He said, "The flesh is of no avail." There is a rather large difference between the two. No one, it is safe to say, would have believed he meant my flesh avails nothing because he just spent a good portion of this same discourse telling us that his flesh would be 'given for the life of the world" (Jn 6:51, cf. 50-58). So to what was he referring? The flesh is a New Testament term often used to describe human nature apart from God's grace.