If you're thinking of the white-card "r4isdhc"... just buy a red box black card "r4i-sdhc", the build quality (including not self-bricking) is superior...

All DS flashcards can do online (if the game is supported by whatever custom servers you're using, and you have a unencrypted or WEP network)
All DS flashcards can do multiplayer either, but (if the receiving consoles are not DS/Lite with flashme) you must turn off all flashcard patches (cheats, ablrxy to quit, etc) for download play