OS X stores folder settings, like view settings and background colors/pictures, in invisible files named ".DS_Store". The problem with .DS_Store files is that they ARE visible on Windows, where they serve no purpose, which is confusing and annoying for Windows users. It seems like Apple has "fixed" this problem by making it so OS X does not create these .DS_Store files on FAT-formatted drives. At least, I have noticed this behavior on my machine. Some quick Google searching reveals evidence to the contrary, however — a lot of people complain that OS X does create these files, and they want it to stop (proof that you can't please everyone!). Some of these complaints are fairly recent, too, so I'm not sure exactly what to think.
The simplest solution would be to reformat as Mac OS Extended (AKA HFS+) and then find some way to use it on the Windows side (I've heard of something called MacDrive).
If you really wanted to, you could manually copy a .DS_Store file from a Mac OS Extended disk to your FAT disk. That would copy over the folder settings, including the background image setting. It's a convoluted process, but it's doable. It would involve creating a dummy disk image, configuring the settings there, going into Terminal and copying the invisible file from your dummy volume to your flash drive. I just ran a little test with disk images, and it seems to work.