Jase. Listen

If you want to play both GBA and DS games on your Nintendo DS flashcart, you will need a SLOT-2 flashcart that supports both types of games. SLOT-2 flashcarts means that the flashcarts go into the slot for GBA cartridges on your Nintendo DS (the bottom slot for GBA carts). One of the best flashcarts for both DS and GBA games is the M3 Lite and the older, bigger M3 Mini SD. It plays both GBA and DS games pretty much flawlessly. There are no SLOT-1 flashcarts that support playing GBA games at the moment (likely, it won't ever happen).

The R4DS you linked to is a SLOT-1 cart that plays all Nintendo DS games for free -- but not GBA games.