Same, my DS Lite still works, but from everything I've read, there ARE no flashcarts capable of playing 3DS ROMs yet. However, certain regular DS flashcarts, like the original R4 running YellowWoodGoblin's WoodR4 firmware, will play regular DS ROMs on a 3DS operating in DS mode. Not sure if it requires old 3DS firmware or not, but you might want to do your own research before buying anything. Flashcarts, by their very nature, can't be guaranteed because while they're not illegal in and of themselves, their usefulness to the honorable art of piracy makes them a target of copyright and high-price/low-value game enthusiasts (EA, Sony, Blizzard, to name a few).
Clarification: WoodR4 is a firmware for the flash cart that serves to provide a sort of mini-OS where you can select from your ROMs, music, pictures, notes, etc. That's right, it makes your DS into a ROM-playing palm pilot :p It doesn't touch the DS and doesn't void your warranty. "Old 3DS firmware" refers to the 3DS's inbuilt firmware potentially having anti-flashcart measures in the newer versions. I don't have a 3DS, so that part I don't know about.