There are plenty of flashcarts compatible with the DSiXl, the Acekard 2i, the EZ Flash Vi...but my recommendation would be the Supercard DSTwo.
[*]The DSTwo can update itself easily, to bypass DSi firmware updates like 1.4.1[*]It has an internal CPU that can emulate GBA games, and SNES games too![*]It also has a video player, capable of viewing unconverted DivX video and FLV.[*]It has a wealth of real-time functionality, like saves, guides, cheats and slow-motion, all better than what flashcarts offer[*]The ROM compatibility is incredible, the DSTwo is capable of bypassing almost every new Anti-piracy so far without flaw[*]Plus, there's an open SDK, letting people make advanced homebrew for the DStwo only.
Seriously? DSTwo is your best purchase, even if it's more expensive than the rest it is totally worth it.
Plus it's the only worthwhile GBA solution for the DSi/XL