If your headphones have an easily-accessible channel running over the head, you can run your ribbon wire through it. Ours didn't so we just tucked the wire against the over-head piece and glued it in place (these Skullcandy headphones have a silicone over-head piece that necessitated a silicone-based adhesive).
Use a pair of tweezers or pliers to gently pull a small amount of wire slack into the earphone through the hole you drilled earlier. This will allow you to easily adjust the headphones without yanking any of your solder joints.
The ring in the same earphone as the FLORA and battery may have to sit a bit closer to the outer plastic of the earphone to allow space for the additional components.
Following the circuit diagram, solder the ring's inner power bus to VBATT on the FLORA main board. Solder the ring's outer ground bus to any pad marked GND on FLORA.
Use tape to stick the ring in position, with FLORA sitting right on top of it. Plug in the charged tiny lipoly and flip the tiny power switch on FLORA to ON. Do all your pixels light up and change color? If so, great! If not, flip it off and check your circuit for shorts or missed connections, and double check your wiring against the circuit diagram.
Make sure FLORA's power switch is set to OFF, and snip one of the battery's wires.
Use heat shrink tubing to insulate these new solder joints.
Tuck the wire connections in and use a little tape and/or Sugru to insulate the FLORA board from the headphone input board. If we had to do this project over, we'd swap the contents of each earphone so that the FLORA main board wasn't so crowded.