If you still have the linker then carry on as normal- the cards should not interfere with each other.
If you mean can my AK2i flash my EZ2 rather than use a PC then no. The only old cart like that can have such things done is the FlashAdvance with FAS1 (which I believe was added into the loader at one point but that is a different matter). Newer devices like the EZ 3 in 1 are however designed to be flashed from the DS slot (you have an EZ2 which is probably one of the most sought after GBA cards out there so no need to switch up).
The DSi is improved hardware vs the DS so definitely not there and all carts that support the DSi and 3ds save the CycloDSi (which people will probably direct you away from) run in DS mode on newer devices so no DSi there either. DSiware (which is downloadable rather than game carts) aside DSi exclusive titles are few and far between (with nothing special either) and all the ones that had extra features on the DSi (DSi enhanced) should still work but work as they do in DS mode (nothing much was added anyway).