I'm making an assumption that every God is a vegetarian? Is the God permitted to consume flesh in his mortal form which is to say his incarnation? Is there any mention in the scriptures to prevent him from doing so?
As far as I understand avataars of Gods for instance Rama, Krishna, Buddha or Kalki are all vegetarians. Read the following from scriptures:
“He is such a great personality that by His mercy He can convert even the meat-eaters [mlecchas] to the devotional service of Kṛṣṇa. Who, therefore, can estimate the power of His Vaiṣṇavism?
Obeisances to Your form as the faultless Lord Buddha, who will bewilder the Daityas and Dānavas, and to Lord Kalki, the annihilator of the meat-eaters posing as kings.
A person fully aware of religious principles should never offer anything like meat, eggs or fish in the śrāddha ceremony, and even if one is a kṣatriya, he himself should not eat such things. When suitable food prepared with ghee is offered to saintly persons, the function is pleasing to the forefathers and the Supreme Lord, who are never pleased when animals are killed in the name of sacrifice.
In the above instance both Krishna and Kalki are avataars and when they are not in favor of something, meat in this case then I don't expect them to consume the same for it would be against their teachings.
Refer the following article here that says:
As long as we look at the over-all evidence of vedic culture, the answer would be a strong NO because vegetarianism has a strong emphasis in the literature especially as we move from the Vedas which focus on karma kanda then move towards the jnana kanda and then we move towards the Bhakti literature then the emphasis and even the insistence of vegetarianism becomes more and more emphatic.
Srila Prabhupada was asked this question about did Lord Ram eat meat? Srila Prabhupada was not at all defensive or apologetic about it. Srila Prabhupada took a different track and He said that Lord Ram is the Absolute Truth. He can eat the whole universe and still will not be affected. So Esha or Lord Krishna devoured the forest fire also. So can we do that?
Garuḍa very clearly eats flesh e.g. that of the Nāga. Garuḍa is a God. So, Yes.
Here Garuḍa is shown explicitly to eat a tortoise and an elephant (after being unsatiated by thousands of Niṣāda) in the Mahābhārata:
https://www.sacred-texts.com/hin/m01/m01030.htm (and the next page). (Astika Parva 29 and 30)
A large part of the Astika Parva is basically a prayer to Garuḍa, who, among descriptions, survives the end of the universe, is capable of destroying the three worlds and is indescribable and inconceivable.
P.S. Garuḍa is the Pakṣīndra (https://templesinindiainfo.com/108-names-of-shri-garuda-ashtottara-shatanamavali-from-garuda-upanishad-lyrics-in-english/)