To Christians and Jews the rainbow and the rainbow flag are symbolical of the promise that God made to Noah
We have to go back to the time of the flood which is written about in the old testament book of Genesis.
Genesis 9:13-16 New King James Version
I set my rainbow in the cloud, and it shall be for the sign of the covenant between Me and the earth. It shall be, when I bring a cloud over the earth, that the rainbow shall be seen in the cloud; and I will remember My covenant which is between Me and you and every living creature of all flesh; the waters shall never again become a flood to destroy all flesh. The rainbow shall be in the cloud, and I will look on it to remember the everlasting covenant between God and every living creature of all flesh that is on the earth.”
Remember that Gods rainbow consists of 7 colour representing his goodness, his mercy, his grace, his love and long-suffering and finally a constant reminder that his promises are true and faithful.
The rainbow is given to remind us of God’s justice in judging sin and His mercy and grace in providing a way to be saved. In addition, the multi-colors of the rainbow can remind us of the splendor of Heaven, and the glorious radiant colors around the throne (as described by the apostle John in Revelation 4
After this I looked, and there before me was a door standing open in heaven. And the voice I had first heard speaking to me like a trumpet said, “Come up here, and I will show you what must take place after this.” At once I was in the Spirit, and there before me was a throne in heaven with someone sitting on it. And the one who sat there had the appearance of jasper and ruby. A rainbow that shone like an emerald encircled the throne. Surrounding the throne were twenty-four other thrones, and seated on them were twenty-four elders. They were dressed in white and had crowns of gold on their heads. From the throne came flashes of lightning, rumblings and peals of thunder. In front of the throne, seven lamps were blazing. These are the seven spirits[a] of God. Also in front of the throne there was what looked like a sea of glass, clear as crystal.
In the center, around the throne, were four living creatures, and they were covered with eyes, in front and in back. The first living creature was like a lion, the second was like an ox, the third had a face like a man, the fourth was like a flying eagle. Each of the four living creatures had six wings and was covered with eyes all around, even under its wings. Day and night they never stop saying:
“‘Holy, holy, holy
is the Lord God Almighty,’
who was, and is, and is to come.”
Whenever the living creatures give glory, honor and thanks to him who sits on the throne and who lives for ever and ever, the twenty-four elders fall down before him who sits on the throne and worship him who lives for ever and ever. They lay their crowns before the throne and say:
“You are worthy, our Lord and God,
to receive glory and honor and power,
for you created all things,
and by your will they were created
and have their being.”