Just getting back to this but wanted to summarize what I did for others finding this thread
1. Take out all the screws from the back side.
2. starting from a corner near the screen pry open the back of the case and work your way carefully along that side and the screen side until the back panel releases.
3. in the corner you will see a large black sticky cover above the mainboard. Peel the edge nearest the side edge back until you see the emmc.
4. Pop the emmc out carefully and replace and press down the black sticky cover.
5. Put the front edge of the bottom panel back in first and then press in from there to the panel edge (basically the reverse of #2)
6. Put the screw back in, the short ones are for the front edge.
Now if like me you want the latest image not something more than a year old then go here.
https://github.com/ayufan-pine64/linux-build/releases
7. download (grab the latest prerelase) and extract the xenial mate pinebook xz image.
8. transfer the .img file to a micro sd card (use the imager or I just use the gnome disks utility on my desktop)
9. Put sd in pinebook and reboot (pw is pine64)
10. Get on a wifi network
11. Now go to the /usr/local/sbin directory, start a terminal and then run this command
sudo pine64_install_to_emmc.sh xenial-mate 0.7.19 (or whatever release you want)
Note: the default is the latest STABLE release which is currently 0.6.x and is now way over a year old so if you don't specify a release that's what you'll get.
12. Remove the sd card
13. Reboot. It's all good now so have a beer and get started customizing your mate install
The only bummer of this procedure is that you've already downloaded the image in step 7 but you have to do it again in the script step 11.
Hope this helps - This really should be in the wiki somewhere instead of buried in some forum post.