noONE - youre an idiot, while it is 100% theoretically possible, i will back my statement up by pointing at the psp app that allows it.
And I will point out that the DS functions entirely different from the PSP. The PSP has an operating system, which the DS does not. This is a major, major difference. With the PSP, even when running an official game, you've got some background code running that drives the entire thing. Homebrew could be running in the background, waiting for a particular key sequence so it could take a screenshot and save it to the media card.
With the DS, once a program has control of the hardware, it has FULL control over the DS. You simply cannot run a homebrew app and a commercial game at the same time; it's not possible.
The only way then would be to patch the rom itself to an extent. Patching a game to do such a complicated task would be troublesome. On the CycloDS forums there is a discussion about this, and Team Cyclops said that they would look into it. The DS can take screenshots, but only of the "primary screen" which is up to the game developer to designate. Most games do not expect to be required to take a screenshot (especially since it requires a full VRAM bank from my understanding) so this may create problems. Furthermore, TC stated that even if they got it working, you would only be able to save a few screenshots at a time, and they'd be stored in raw format temporarily on the CycloDS Evo itself until the next bootup, when it would convert them to a PC-friendly format and store them on your card.
So yes, in theory it's possible, but not by means of a homebrew application. Only hardware hackery with the homebrew devices themselves will make it a possibility.