You're correct, God did grant permission to eat animal flesh, but that was part of the concession He offered because of the hardness of the human heart. However, this did not change God's original intent that humans and other animals should live a vegan lifestyle.
Please take a look at:
Living in the Will Rather than the Concessions of God
Genesis 8:20-22
Genesis 9:1-4 - A Commentary on God's Concession
In the Love of the Lord,
Frank and Mary