Not possible, sorry. The DS doesn't have an operating system running in the background like the PSP does, so it's impossible to run a screenshot program and an actual game at the same time.
If you have an official NITRO video capture device, you could get screenshots, but that's all for now. The CycloDS Evolution developers were considering adding support for this to their firmware, allowing you to take a couple of screenshots per gaming session, but I don't know if anything came out of that. At the very least, it would have to be implemented by the hardware developers, so it's not something homebrew coders can accomplish on their own.
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