This question is mainly for Hindus but open for anyone who would like to offer some respectful thoughts or insights.
The Baha'i faith teaches that Krishna was a 'Manifestation of God' and is ranked alongside other Great Spiritual Teachers such as Buddha, Christ and Muhammad.
Manifestations of God | What Bahá’ís Believe
Manifestation of God - Wikipedia
Bahá'í Faith and Hinduism - Wikipedia
We have a few scant references to Krishna and Hinduism in our writings or from the talks of Abdu'l-Baha. For example:
Blessed souls whether Moses, Jesus, Zoroaster, Krishna, Buddha, Confucius, or Muhammad were the cause of the illumination of the world of humanity. How can we deny such irrefutable proof? How can we be blind to such light?"
('Abdu'l-Bahá from a Tablet - translated from the Persian)
The Message of Krishna is the message of love. All God's prophets have brought the message of love....
("Paris Talks: Addresses given by `Abdu'l-Bahá in Paris in 1911-1912", 11th ed. (London: Bahá'í Publishing Trust, 1979), p. 35)
So in summary we haven't a lot to go on when it comes to Krishna.
In regards Hinduism Shoghi Effendi has said:
...Hinduism, Buddhism, Zoroastrianism, Judaism, Christianity, Islám and the religion of the Sabaeans. These religions are not the only true religions that have appeared in the world, but are the only ones which are still existing. There have always been divine prophets and messengers, to many of whom the Qur'án refers. But the only ones existing are those mentioned above.
In regards the authenticity of the sacred writings including the Bhaghavad Gita we don't have too much to go on either. In response to questions of a more detailed nature Shoghi Effendi said it would be a matter for scholars to investigate further.
Your question concerning Brahma and Krishna: such matters, as no reference occurs to them in the Teachings, are left for students of history and religion to resolve and clarify.
(From a letter written on behalf of Shoghi Effendi - 14 April 1941)
We cannot be sure of the authenticity of the scriptures of Buddha and Krishna, so we certainly cannot draw any conclusions about virgin birth mentioned in them. There is no reference to this subject in our teachings, so the Guardian cannot pronounce an opinion.
Buddha, Krishna, Zoroaster and Related Subjects
So in regards Krishna we haven't anything specific from the Baha'i writings to say. In fact we don't have much to say about Hinduism other than it is a true religion with Divine origins.
So who was Krishna? What do we know of Krishna from history and Hindu traditions?
I belong to Ahmadiyya peaceful Islam. We believe that Krishna was a prophet/messenger of G-d.
1. Irrespective of the objections of the Hinduism religions, we have to believe in the truth of Krishna as a truthful prophet/messenger of G-d as a principal article of our faith, if we deny their being prophets/messengers of G-d, we cannot be Muslims.*1
2. Denial of one prophet/messenger of G-d is denial of all the prophets/messengers of G-d as they are all sent by G-d. And denial of one of them is denial of G-d who has sent them.*2
3. Prophets/messengers have been sent to all the peoples of the World from themselves as Warners and as Guides.*3
4. Quran mention that only some prophets/messengers of G-d has been mentioned in Quran, and there are others that have not been mentioned.*4
5. It is a wrong notion that only prophets/messengers of G-d from the off-spring of Abraham have been mentioned in Quran. Luqman and Zul-Qurnain (Cyrus the Great of Persia, a Zoroastrian) are two examples.
Regards
*1
[2:5]
And who believe in that which has been revealed to thee, and that which was revealed before thee, and they have firm faith in what is
yet to come.
[2:6]
It is they who follow the guidance of their Lord and it is they who shall prosper.
The Holy Quran - Chapter: 2: Al-Baqarah
*2
*[11:60]
And these were ‘Ad. They denied the Signs of their Lord and disobeyed His Messengers and followed the bidding of every haughty enemy
of truth.
The Holy Quran - Chapter: 11: Hud
[2:286]
This Messenger
of Ours believes in that which has been revealed to him from his Lord, and
so do the believers: all
of them believe in Allah, and in His angels, and in His Books, and in His Messengers,
saying, ‘We make no distinction between any of His Messengers;’ and they say, ‘We hear, and we obey.
We implore Thy forgiveness, O our Lord, and to Thee is the returning.’
The Holy Quran - Chapter: 2: Al-Baqarah
*3
[13:8]
And those who disbelieve say, ‘Wherefore has not a Sign been sent down to him from his Lord?’ Thou art, surely, a Warner. And there is a Guide for every people.
The Holy Quran - Chapter: 13: Al-Ra`d
*4
[40:79]
And We did send Messengers before thee; of them are some whom We have mentioned to thee, and of them there are some whom We have not mentioned to thee; and it is not possible for any Messenger to bring a Sign except by the leave of Allah. But when Allah’s decree came, the matter was decided with truth, and then there perished those who uttered falsehoods.
The Holy Quran - Chapter: 40: Al-Mu'min