First up, solder sturdy wires to the NeoPixel Matrix. This thing draws a lot of current, so solid connections are an absolute must! To evenly distribute the power, connect up all the GNDs to each other, and likewise with the 5v pads. You can twist two pieces of wire together, tin the twist and the pad, then reheat both together to join. The input side wil look like this:
Solder your free 5v connection to VBATT on Flora, and your spare GND conenction to GND on Flora. The data input pin should be soldered to pin D12.
Load up the NeoPixel Matrix demo sketch, change PIN to 12, connect the battery, and make sure you see a message scrolling across the display before proceeding! It's much easier to troubleshoot problems incrementally than it is to wire everything up and try to identify a wiring error later.
If you get errors when trying to upload to Flora, be sure you have the NeoMatrix, NeoPixel, Adafruit BusIO and Adafruit GFX libaries for Arduino installed, and that the right board and serial port are selected. You can install libraries directly from the Arduino app under Sketch -> Include Library -> Manage Libaries (Arduino 1.6.4 and above).
When your matrix is up and running, you can disconnect the battery and USB cord and protect the wire connections on the matrix with E6000 adhesive. While you're at it, squeeze some adhesive into the top of the battery, where the wires connect, for some strain relief. Allow glue to dry for 24 hours.
Next, solder up the connectiosn to Fona according to the circuit diagram. Attach the GSM antenna to Fona, and the battery to Fona's JST port.
Add some Velcro tape to secure the battery. Your finished circuit should look something like this: