There are two Bible verses that mention rainbows in heaven.
Revelation 4:3 mentions a rainbow around the throne of God.
And he who sat there had the appearance of jasper and carnelian, and around the throne was a rainbow that had the appearance of an emerald.
Revelation 10:1 mentions a rainbow over the head of an angel.
Then I saw another mighty angel coming down from heaven, wrapped in a cloud, with a rainbow over his head, and his face was like the sun, and his legs like pillars of fire.
So based on these verses, the answer to your question is: maybe.
You’ll notice that in both verses there is a singular reference “a rainbow,” not a plural reference, “rainbows.” And yes, these verses clearly use the word “rainbow.” So here is why my answer is maybe. I don’t think it’s a stretch to understand your use of the word rainbow as a multicolored arc we see in the sky. Here’s the rub. The word “rainbow” in these two verses comes from the Greek word iris. This is where we get our English word “iris,” such as the “iris” of the human eye which defines our eye color or “iris” as a plant genus with many colorful species under it. According to an authoritative Greek lexicon the word iris means, “an arc or circle of light, whether colored or not” and could also be translated “halo” or “radiance” (A Greek-English Lexicon of the New Testament and Other Christian Literature, 480). So do the rainbows mentioned in Revelation 4:3 and 10:1 refer to the colorful rainbows we’re used to seeing in the sky or are they a halo of light without color? Well, the reference in Revelation 4:3 seems to include color because it says that the rainbow “had the appearance of an emerald” suggesting that it is green. As for the rainbow over the head of the angel there is simply no mention of color.
I will offer one final note on the significance of rainbows. Rainbows have more than mere sentimental value. The rainbow is significant because it is the sign of the covenant the Lord made with Noah in the Old Testament after the worldwide flood. Genesis 9:8-17 provides the details of this covenant,
Then God said to Noah and to his sons with him,  ‘Behold, I establish my covenant with you and your offspring after you,  and with every living creature that is with you, the birds, the livestock, and every beast of the earth with you, as many as came out of the ark; it is for every beast of the earth.  I establish my covenant with you, that never again shall all flesh be cut off by the waters of the flood, and never again shall there be a flood to destroy the earth.’  And God said, ‘This is the sign of the covenant that I make between me and you and every living creature that is with you, for all future generations:  I have set my bow in the cloud, and it shall be a sign of the covenant between me and the earth.  When I bring clouds over the earth and the bow is seen in the clouds,  I will remember my covenant that is between me and you and every living creature of all flesh. And the waters shall never again become a flood to destroy all flesh.  When the bow is in the clouds, I will see it and remember the everlasting covenant between God and every living creature of all flesh that is on the earth.’  God said to Noah, ‘This is the sign of the covenant that I have established between me and all flesh that is on the earth.’
It appears that the rainbow mentioned in Genesis 9 is the same rainbow, a multicolored arc, we’re used to seeing in the sky. Every time we see a rainbow, then, it is God reminding us that He will never destroy the world by a flood again. God is gracious in dealing with mankind and faithful to keep all His promises. The rainbow is therefore a reminder of the graciousness and faithfulness of God.
In conclusion, there are two verses in the Bible that mention rainbows in heaven though it is difficult to determine if they are the same multicolored rainbows we’re used to seeing. However, the significance of the rainbow is important. It is a sign of God’s promise to deal graciously and faithfully with mankind. Now that’s something that adds color, even to rainbows.