You can definitely change out the battery although its clear the mfg would rather you buy a new flip for $165.00.
Remove the cover very slowly and carefully so you don't break the ribbon cable. You can then unplug one end of the cable and leave it in the socket on the other end. Carefully fold over the display and be careful because the mylar backing is glued down. After folding it over, you can access two of the four screws that hold down the circut board.
You don't need to remove the two screws holding the USB flip connector.
Remove the battery following the ifixit procedure but be careful not to break the tiny power wires at the top of the circut board. Only slightly elevate the bottom of the board and, after unscrewing the metal battery carrier and carefully unplugging the battery connector, you can pop out the battery. You will need to use a long thin knife to carefully pry the battery from its carrier as it is glued in place w/ sticky tape.
Go to Batteries Plus and get the battery and replace it following reverse procedure.
There you have it :)