I am doing a test on a few common Flash Cards, forgive me if I have forgotten some, I will try and add them in later:
Also don't let this deter you if it states your card is not compatible, please try anyway and notify us if I am incorrect.
Desmume: Working (0.9.7+)
Acekard 2i: Working (On latest 1.8.9 Acekard firmware)
DStwo: Working (On latest DStwo 1.16 firmware)
R43DS: Working (On latest v1.58b firmware)
CycloDS: Working (2.30)
R4i Gold Pro: Working, needs modifying (1.49.2 firmware), Press "Y" and then "X" with game selected and change settings so "reset in game" is off.
R4i Dual Core: Working, needs modifying (1.49.2 firmware) Press "Y" and then "X" with game selected and change settings so "reset in game" is off.
R4 Revolution/Non SDHC: Working, needs modifying (Latest Wood r4) Press "Y" and then "X" with game selected and change settings so "reset in game" is off.
R4isdhc-silver: Not working currently (Firmware 1.30.2) Please notify me if you get it to work.
EZ Flash Vi Working (Latest firmware).
The cards that are "working but needs modifying" currently have a bug where you cannot enable the c gear without crashing the game. Make sure you save after the first gym straight away as a precaution in case you forget to select "No" when it asks to enable C Gear.
Keep in mind this may not be 100% the same for everyone, I am basing this on my results and that of people in the IRC.