Except that flesh and blood does not inherit the kingdom of heaven.
"Flesh" (and "blood") sometimes refer to sinful human nature, deprived of grace. In that sense, "flesh and blood" will not inherit the kingdom of heaven.
Nevertheless, the term "flesh" retains its primary meaning of, simply, flesh--i.e., the body.
The very beginning of Saint John's Gospel tells us that "the Word became flesh, and dwelt among us." Saint John was NOT telling us that Word became "sinful human nature"! He was telling us that the Word became united with a HUMAN NATURE. I.e., the Word became a man.
Since the FLESH or BODY of Jesus that is present in the Eucharist is the same flesh or body or human nature that St. John is referring to when he says "the Word became flesh," obviously the body and blood in the Eucharist are NOT "sinful human nature," but are the sinless human nature of Jesus Christ.
And where is any mention of the blood in that comment?
The blood is what redeems us.