fine if you are asking if homebrews will work then yes. all homebrews work on all flash carts. you will probably have some difficulty getting the flash cart to work, but if/when you get the flash cart running you can run any homebrew that is a .nds file....
The R4DS does not have any official support since 2008, but users have adopted ysmenu/dstt in order to play the latest software, this is also close to an end. The original R4DS also only supports 2gb sd card and no dsi. R4i cards are all clones...
Try formatting the micro sd with the Panasonic format program. Do a full format, not just a quick one, that usually helps. Second thing that might help is trying alternative software versions. When you boot your DS with the memory card without...