Start your QNAP device and login via SSH. Some time after you start your machine, you will hear a beep and a bit later you'll hear a longer beep. Wait for a few more seconds and then connect to the machine via SSH. The username is admin and the password is admin too.
Once you are logged in, you can save the content of your flash partitions to a USB stick. Connect a USB stick to your QNAP and wait for the system to mount it. In my case, it was mounted at /share/external/sdi but you can find the location with the following command:
mount | grep external
/dev/sdi1 on /share/external/sdi type vfat [...]
Now go to this directory and make a backup of your flash partitions:
cd /share/external/sdi
cat /dev/mtdblock0 > mtd0
cat /dev/mtdblock1 > mtd1
cat /dev/mtdblock2 > mtd2
cat /dev/mtdblock3 > mtd3
cat /dev/mtdblock4 > mtd4
cat /dev/mtdblock5 > mtd5
cd
umount /share/external/sdi
Disconnect your USB stick from your QNAP, connect it to your PC and to add the mtdX files to your regular backup.