The three principle Biblical passages which make use of the image of the rainbow are the passage in Genesis (Noah), the section of Ezekiel in my last post, and the 10th chapter of Revelations:
 And I saw another mighty angel come down from heaven, clothed with a cloud: and a rainbow was upon his head, and his face was as it were the sun, and his feet as pillars of fire:
 And he had in his hand a little book open: and he set his right foot upon the sea, and his left foot on the earth,
 And cried with a loud voice, as when a lion roareth: and when he had cried, seven thunders uttered their voices.
 And when the seven thunders had uttered their voices, I was about to write: and I heard a voice from heaven saying unto me, Seal up those things which the seven thunders uttered, and write them not.
 And the angel which I saw stand upon the sea and upon the earth lifted up his hand to heaven,
 And sware by him that liveth for ever and ever, who created heaven, and the things that therein are, and the earth, and the things that therein are, and the sea, and the things which are therein, that there should be time no longer:
 But in the days of the voice of the seventh angel, when he shall begin to sound, the mystery of God should be finished, as he hath declared to his servants the prophets.
 And the voice which I heard from heaven spake unto me again, and said, Go and take the little book which is open in the hand of the angel which standeth upon the sea and upon the earth.
 And I went unto the angel, and said unto him, Give me the little book. And he said unto me, Take it, and eat it up; and it shall make thy belly bitter, but it shall be in thy mouth sweet as honey.
 And I took the little book out of the angel's hand, and ate it up; and it was in my mouth sweet as honey: and as soon as I had eaten it, my belly was bitter.
 And he said unto me, Thou must prophesy again before many peoples, and nations, and tongues, and kings.
The passage in Revelation like the passage in Ezekiel ends a vision with a voice calling to prophesy. Blake has once again chosen to illustrate the passage literally. We see with our eyes what John of Patmos saw as vision: the angel, the cloud the rainbow colors, the radiance of the face, the right foot and left foot on sea and earth, the little book in the left hand, the seven thunders as horsemen in the dark cloud and feet as pillars of fire. John himself is seen between the feet of the angel recording as directed.
The rainbow is one of many clues that this event of transition, the Revelation of the Apocalypse, is to link God and man. As a covenant was announced with the first rainbow appearance to Noah, a new dispensation is announced in Revelation. A new spiritual Jerusalem will replace the former Jerusalem whose temple had been intended to link God and man.
Blake's Vision of the Last Judgment provides us with images in words and pictures of the new dispensation which emanates from the Last Judgment. Blake includes these images of the new Jerusalem which is to replace the mortal with the immortal.
Vision of the Last Judgment,(E 561)
"The Cloud that opens rolling apart before the throne &
before the New Heaven & the New Earth is Composed of Various
Groupes of Figures particularly the Four Living Creatures
mentiond in Revelations as Surrounding the Throne these I suppose
to have the chief agency in removing the
old heavens & the old Earth to make way for the New Heaven & the
New Earth to descend from the throne of God & of the Lamb."
Vision of the Last Judgment, (E 562)
"Jesus is surrounded by Beams of Glory in which are
seen all around him Infants emanating from him these represent
the Eternal Births of Intellect from the divine Humanity A
Rainbow surrounds the throne & the Glory in which youthful
Nuptials recieve the infants in their hands"
Perhaps the rainbow should always be seen as an invitation and a promise such as Blake issues here:
Vision of the Last Judgment, (E 560)
"If the Spectator could Enter into these Images in his
Imagination approaching them on the Fiery Chariot of his
Contemplative Thought if he could Enter into Noahs Rainbow or
into his bosom or could make a Friend & Companion of one of these
Images of wonder which always intreats him to leave mortal things
as he must know then would he arise from his Grave then would he
meet the Lord in the Air & then he would be happy"