I suggested earlier that various texts use the word 'sign' or 'mark' (Hebrew 'ot or Greek semeion) to refer to priests (specifically, Genesis 1, Genesis 4, and Isaiah 8). Now Genesis 9 give us an interesting test, where it identifies the 'token' (again, 'ot and semeion -- the English translation is different, but the Hebrew and Greek are the same term as the other texts) of the eternal covenant (brit 'olam), as a bow set in the clouds. A rainbow.
Cloud imagery is common of texts set inside the temple: for starters, the Mount of Transfiguration, Daniel 7, and Lehi's dream. This reflects the incense altar that was set in the hekal, the middle room of Solomon's Temple. But are there any texts that corroborate the idea that a rainbow might refer to a priestly figure?
Turns out there's at least one. Chapter 50 of Sirach, a book preserved in the LXX but not the MT, shows the coming forth of a priest named Simon son of Onias in a temple setting (scholars think on the Day of Atonement). Verses 5-7 read like this: "...how he was glorified as he spun around the shrine, as he exited from the house of the veil. Like a morning star in the midst of a cloud, like the full moon in the days of a feast, like the sun shining on the shrine of the most high, like the rainbow gleaming in clouds of glory..."
We have: the specified location in the temple; clouds; comparison of the priest with astral bodies, like 1 Nephi 1 (stars = angels = priests); and the identification of the priest with the rainbow.
So I think the message of Genesis 9 is not that as long as you see rainbows, God won't flood the earth, but when rainbows cease, we might be in trouble (this was the folklore I knew as a kid, and believe me, I looked for rainbows with great anxiety). I think the message of Genesis 9 is that the sign, 'ot, of the eternal covenant, is that the Lord appears to his people in the temple. In ordinances, he does this in the person of his authorized messenger, the Melchizedek priest.