You can emulate DLDI for homebrew.
Flashcart as far as being able to run a loader (presumably to take screenshots or something of random flash carts) then not so much. You would be far better off figuring out what it needed to boot and booting that; sometimes it is just a matter of disabling a few checks it does, other times they will have things to prevent their data from being copied by other teams and you would then have to defeat all that.
If you can find some way of dumping memory then you could either reconstruct things or hack it a bit to add a screenshot function. Most times it is flash carts themselves that have the savestate function though so that is tricky. Don't know what the old cheat making devices will have here.
Alternatively with things like the jumbotronDS and later 3ds capture cards they worked at the hardware level with the options to capture things.
Though you are still left with having to run the flash cart kernels and at that point emulation is probably back in.