Probably the CycloDS iEvolution. The original CycloDS was quite popular, but the iEvo never seemed to sell much. I still have one sitting around here somewhere... It's certainly the rarest one I have, but probably one of the rarest overall as well.
A lot of the early DS flashcarts (pre-R4) didn't seem to sell well either, for example I've never heard of anyone who actually owned a NinjaDS flashcart (this one was an odd one, it was the same shape as a normal DS flashcart, but twice as tall, making it look like some obscure official development hardware) and there were other oddballs like it, like the Datel Max Media Dock, which also had quite an interesting form factor, but was a lot more popular in its time.
The DS-X seemed to be the most popular of the early DS flashcarts, there were quite a lot of people who bought it talking about it here back in the day, I don't think that one quite counts as rare, unless all those people that bought one threw it in the garbage (or it broke) and they bought an R4 instead. Dancing LEDs aside, it was a great flashcart at the time, with some unique features. The thing that held it back and quickly made it inferior was the limited, non-expandable storage.
I don't know why so many people mentioned the DSTWO. That thing sold in droves, it's anything but rare. People who have one just don't want to get rid of it. I know I'm never getting rid of mine
The DSTWO+ is a little more rare, as it wasn't on the market for nearly as long, and seemed to be disliked because of the Gateway clone functionality and the brick risks associated with it.
But maybe the GBAtemp edition DSTWO? I don't know if it counts as a separate flashcart, but it was a limited edition.