The first part isn't talking about eating flesh in general. When it says "Ye eat with the blood" it means that they ate the flesh without first draining the blood. If you look at the laws in Leviticus, it shows that it is a sin to eat the flesh without first draining the blood, because blood is the life.
 And whatsoever man there be of the house of Israel, or of the strangers that sojourn among you, that eateth any manner of blood; I will even set my face against that soul that eateth blood, and will cut him off from among his people.
 For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul.
 Therefore I said unto the children of Israel, No soul of you shall eat blood, neither shall any stranger that sojourneth among you eat blood.
 And whatsoever man there be of the children of Israel, or of the strangers that sojourn among you, which hunteth and catcheth any beast or fowl that may be eaten; he shall even pour out the blood thereof, and cover it with dust.
 For it is the life of all flesh; the blood of it is for the life thereof: therefore I said unto the children of Israel, Ye shall eat the blood of no manner of flesh: for the life of all flesh is the blood thereof: whosoever eateth it shall be cut off.
 Only be sure that thou eat not the blood: for the blood is the life; and thou mayest not eat the life with the flesh.
 Thou shalt not eat it; thou shalt pour it upon the earth as water.
 Thou shalt not eat it; that it may go well with thee, and with thy children after thee, when thou shalt do that which is right in the sight of the LORD.
Itinual Praises unto Jah RasTafarI Haile Selassie I Menen I