That sounds about right; the fan-made port of KS for the DS would probably work on a DSi (and maybe a 3DS while in DS mode, but I have no idea about the new one). My limited understanding of the matter is that the "New" 3DS can also play DS games- and so if there's a flashcard that would work and can boot such a thing, then the custom KS port may work. Nintendo has a habit of locking flashcards out of their systems- I don't think people have actually managed to get DSi-specific features easily working on homebrew, and the DSi isn't exactly new (namely, that'd be the camera and better wifi capabilities, I think?). My point is, I don't know how reliable any suggestions of using homebrew on a 3DS are. Since they often update the 3DS systems with new firmware, what may work today may not tomorrow. If either the 3DS or the New 3DS have a flashcard that can launch a DS-mode application, then it probably would work. I can't tell if/what that may be, though.
To further dive into the question; I believe the port of KS had some technical challenges since the DS can't just load a lot of graphics and things like a computer, so I don't know if things like the custom animated objects were ever supported (as the key example). A lot of levels ended up using those small features that were added in the last official KS version. If you do manage to play the port on the 3DS, it'll only look (and play) as good at the port did on a DS, since that's what it was designed for. It seems pretty unlikely there will be an update for the 3DS at this point (or any updates; I don't think I've seen that user around much). For the same reason, a full Vita homebrew port doesn't sound likely for the same reason, although I thought the same user was doing/did a PSP port as well.. But, again, Sony has their stuff just as locked as Nintendo and unfortunately, I'm not aware if the Vita has a 'backwards compatibility' mode for the PSP, which means it'd have to be re-made.
I might as well also say that an official port of Knytt Stories to anything seems pretty unlikely; I think Nifflas is fairly satisfied with how far Knytt Stories has gone, and it would be hard for him to just port it to entirely different hardware types (particularly if it's limited to being homebrew which is easily broken by gaming manufactures). I wish there was a more optimistic "yes, sure!", but the truth is that it's trial and error, and whichever way it is, it'll only work by running the existing version which is only for a DS (again; maybe a 3DS card will run it via DS mode, which would be awesome; but I don't know).