mount the drive with pmount (or pmount-hal)
where sdX is the device
You need to mount it as the user you want to be able to write to it. You could do this with mount options (like uid=username).
The reason you can't change permissions is because (as you thought) vfat doesn't support permissions, it's just a limitation of FAT.
If you mount the device a lot, then you may consider adding a line to /etc/fstab for it. But that will only work if the device always has the same name in /dev