What does formatting a slot 1 card mean?
What is the name of your Slot-2? And what happens when you try to boot it?
I imagine you could make something that writes to the onboard storage via DSi homebrew SD access or wifi on the original DS (or DSi as well I guess). Nothing I am aware of is geared towards doing it though -- obvious first step would be to find something the DS FTP servers or file system management tools.
It would be better at this point to ditch the piece of junk flash cart you have and get almost anything else.