Your best bet is to use an PC based emulator. Given it's additional processor, i'm guessing the DSTWO may technically be capable of doing that. You could ask on the supercard forums for it to be added as a feature.
The only thing I know of is Moonshell, but that only takes screenshots of Moonshell.
IIRC there are carts that have ingame menus, M3iZero I believe, that can do 'basic' stuff like cheats (and I think I heard they can open small text documents?) so it doesn't sound out of the realm of possibility... but improbable is more likely because it would have to be done at the flashcart level not application level.
Well...there IS that $3000 machine...NITRO IS Capture or something...but that is a rare thing to come by and you supposedly can only get one if you are a developer. Apart from that, I've only heard of Moonshell2 having screencapture...(though probably M3Sakura and the EzFlashV have the ability possible since both are based off of MS2)
Hmm well this would be an amazing thing because i got the model viewer working but it would be better if it would capture the screen and save it to a card so i wouldn't get banding errors (note this model is not mine i just used it for testing purposes)
If you're writing the DS homebrew program yourself, you can code in the ability to take screenshots, as there's a built-in function in libnds to do that. It will take a screenshot of the main screen (which you as the programmer have defined).
If you're trying to get screenshots of something that doesn't have that ability already coded in (such as any commercial game) then it's not going to be possible unless a flash cart maker adds the ability to their own cart. Because the DS only runs one application at a time, you're not going to see a generic "screenshot taker.nds" program that can grab screenshots of Mario Kart DS or anything like that.