White screen when I launch my R4i+ 3DS/DS

Do you mean that the card was previously working on both 3DS units, and has now stopped working? Or have you never been able to get this card to do anything?

If all else fails you might consider using TWiLight Menu to launch your DS games instead.

 

Use this and then try to load your flashcard again

 

Do legitimate DS cartridges still work on both units?

TWiLight Menu loads DS games from the SD card inside the 3DS. There are some cases in which a flashcard still works better, but not too many. (Of course it requires CFW to be installed.)

 

Perharps it could be a problem with the microSD of the flashcard or the kernel.

Please check if the microSD has FAT32 format (or FAT, if its size is less of 2GB) and put the kernel files and folders on its root. And also check if the microSD is adequately inserted into the respective slot on the flashcard.

PS: You can (re)format the microSD card for the flashcard following this tutorial, if you want

 

I haven't used a flashcart but have you tried the old, remade, bluecardfix?

 

If @Kamanberu has a console with Luma CFW (on its latest version 10.2.1), there's no need to install/use that bluecardfix thing, because Luma itself applies all the required patches to remove the DS mode flashcards blocking (or whitelist applying) by default

 

Good to know!