Next I put some teflon tape around the nipple and used that to connect the coupling to the ball valve. Make sure that the ball valve is arranged so that when the handle is open, it's pointing away from the cooler.
Next up I added the barb to MIP adapter with some teflon tape on it as well. MIP stands for Male Iron Pipe so that should be 3/8" to match the ball valve, but if you are using a different sized line than 3/8" you might need to get a different adapter.
I then narrowed one end of the braid by pulling it tight (think Chinese fingercuffs) so it would fit through the flare nut. Once through, I spread out the end enough to go over the Flare MIP Union and tightened the flare nut.
The braid assembly screws into the inside of the coupling. I didn't tighten too much just because I want to easily take it out in case I need to use this cooler as an actual cooler.
I left the braid at it's full length for now because I'm not sure if the extra length is beneficial or harmful for batch sparging.