
Spoiler:
If your really wanna know. I can tell you whether the two of them die because this manga already got licensed in my country quite some time ago. Hence I already bought and read all the 27 volumes a few times.
So coming back to the point.
Both Kinrei and the Prince will live on - so you can be happy! (⌒▽⌒)
(even though they die along with Rakan and Chigusa in their last battle with them at first. However they get back to life after some time and with the help(or better to say is with the life) of the Sanome woman which resembles Rakan's mother)
After their resurrection the Prince and Kinrei go to live in the underground in the room in which Hoshiminokoto lived before.
There they want to regulate the sand which Hoshiminokoto used for keeping alive his consciousness (and doing other stuff) on Chigusa's proposal.
There is also quite a cute scene between the Prince and Kinrei in the last volume (at least in my opinion). So look forward to it ლ(´ڡ`ლ)

Yes! :)

Spoiler:
As the one who answered you before me they do come back to life even though only the ones close to Rakan and Chigusa will know that because they don't want the people do get dependent on a godlike being again.
Hence, Rakan and Chigusa return to Rakans former world to live in that one. Chigusa even gets a job in something like a coffee shop.
Also from time to time Narushige and Touji and some of the others visit Rakan and Chigusa. Naturally these two also come to visit the others in the other world too. ^^
i really hope nothings bad gonna happen to kinrei or the prince. i really ship them both and want them to live happily. tho i kinda have a feeling that kinrei will die or something.....