Normally, mounts are writable only by the user who mounted them (use the "users" option to allow mounting by any user).
To set a different permissions mask on the drive, use the "umask" option. Any permissions not in the mask will be set for the files on that mount. Since FAT doesn't have native permissions, the permissions of all the files on the FAT partition will be the opposite of what you set on in the mask.
For example, I use the options "umask=000,quiet,users" for floppy drives. What this means is:
"umask=000": let everybody do everything (equivilent to "chmod a=rwx" or "chmod 777", remember that dirs need to be executable)
"quiet": don't print out those annoying warnings about permissions, since FAT won't allow you to set them. (This is also why your chown command failed, BTW)
"users": allow anybody to mount the partition.
Whatever options you set go in place of the "defaults" in your fstab line.