" Jesus said to them, “Very truly I tell you, unless you eat the flesh of the Son of Man and drink his blood, you have no life in you. Whoever eats my flesh and drinks my blood has eternal life, and I will raise them up at the last day. For my flesh is real food and my blood is real drink. Whoever eats my flesh and drinks my blood remains in me, and I in them. Just as the living Father sent me and I live because of the Father, so the one who feeds on me will live because of me. This is the bread that came down from heaven. Your ancestors ate manna and died, but whoever feeds on this bread will live forever.”Read it out loud, and I think you'll be on your way to "getting" it. He could hardly say, "Eat My Flesh, it avails nothing!" or... "Don't bother eating My Flesh, it's not good for anything!"
When He says "the flesh" avails nothing, He means YOUR flesh, an earth-bound understanding, unaided by the Grace of God. He often uses "the flesh" this way, to mean a narrow, materialist mind-set, un-illumined by faith. It's like saying "You meat-head!"
If HIS Flesh meant nothing, it would mean His coming in the flesh (incarnation) was useless, as well as His dying in the flesh (the atoning sacrifice) and His rising in the flesh. This obviously means a great deal, HIS Flesh. It means everything.