For the corners we have the Blasted Craters, the Devil's Scab, and the Mossteeth, the three showing the edges of our domain.
In the top left there is the crecent moon DB wanted. I used m1895's design for them, so you can expect the lore from that. A simple version of the moon we worship and the stars of the night sky.
The centerpiece is the representation of our capital, a pool reflecting the moon and stars above to represent the lore you wrote. The brown is the earth we cultivate and shape, followed by the canals which are used to transport water. Followed by the desert itself.
The bottom arrow represents Water of course. The right is crops, fruit of the land as it were, and the earth.
The top represents the sun, though being night it isn't bright yellow right now.
The left arrow was the multi-gradient that represented our people as a whole. For this version it's simply a sunset orange surrounded by the color of the desert sands during the day.
The circle surrounding the pool is more a remnant of the original capital representation, though it's also the color of the desert sands during the night. And the pool. That one simply reflects the vision above as water does. Though one could also say it represents the touch of the moon in us all, if being poetic about it.
Not much more to say, though from the beginning when I read the lore for inspiration, Chaos stuck out to me. While it doesn't actually have 8 arrows, I think the four images in the corner substitute, and the other four remain a core part of it.
It also looks like a compass, but... That's not the focus of it. The dark blue makes a nice contrast color for the flag.
More simply. In to out goes..
Our Center of Magic> Capital Buildings> Canals> Desert.
Water/Life Arrow, Earth/Crops Arrow, Sun/Fire Arrow, People of Luna/(Wind) Arrow.
Blasted Craters, the Devil's Scab, and the Mossteeth. Pax Alikai and the three main stars foretelling our victory.
And dark blue background to evoke a sense of night to go with the moon.
Thinking on it, fire is something most civilizations learn, so the Sun being connected to Fire isn't bad.
So the desert folk being tied to the concept of wind does create a four element ensemble rather neatly.
Fire for the Craters, Earth for the Scab, Water for the Mossteeth, Wind for the desert. Very neat. The moon would be light/divine in folklore if this were a story.
Should proobly go to bed, too easy to make connections, though they were there before anyway but for wind.
... Hua, one more. The arrows can be considered the traditional four gates in the city walls. I piled a lot into the original flag once I got going, though mostly a result of that one symbol being the capital. You might write a more concise flowery version than me. I tend to ramble. Night.