3DS flashcart: http://www.thegamerdepot.com/
At first, to answer the questions, no. there's absolutely no possible way to load a 3DS rom file, although they're uploaded online. Currently all the DS flashcart will only let you play DS games, can not play not even one 3ds game.
There was a rumor says that ace3ds pro flash cart can play 3ds games, but looks like it is just a rumor, have talked with some of my friends. the ace3ds pro is not a real 3ds flashcart. it is just a normal flashcart and attach with one 3ds game, the baseball game. and you can only play one 3ds game with it. and you can exchange it to other games. So this is just a real 3ds game and insert one flashcart. What's more, the baseball game is even a Jap game. so you even can not use it on the US or EU consoles. So it is no use. there is no source shows there will be more 3ds games with this kind of card, we will just see what will happen, but for now, still no flash cart can do it.
It is not easy to play 3ds games on the 3ds with a flash cart. 3ds hasn't been hacked yet, so there is no way to create a fash cart can do it. I am sure many guys are working on it, but so far, no good news. We just hope it will come out asap.
For now, i suggest everyone just get a normal ds flashcart and play all the ds games. when the 3ds is really hacked in future, you can just update the flash cart to play 3ds games on 3ds with flashcart. The best flashcart for now is the Supercard dstwo or r4i gold 3ds cart.