i want to run a 100 percent braided line from the trans to the cooler and back would this part work for the transmission side or would i need this and this

 

The banjo bolt won't work.

 

I know at least the trans uses 5/16" flare fittings.

 

None of those will work. The fitting going into the transmission case is 1/8 NPT.

I simply used the factory lines and cut them about 2" off the transmission. I just slid the steel braided lines over the tubes and secured them with hose clamps. With limited access and a tranny shield, loosening the hose clamps makes removing the cooler lines so much easier.

 

I thought a 5/15th fitting had 1/2 20 threads i could be wrong tho

 

1/8 npt in trans.
5/16 lines and ends.
wouldn't ever recommend anything but solid line in between such large gaps. connections yes, but not for long distances. Note: trans fluid is very flammable, it will catch you, your car, or both on fire if not handled properly. I know this might sound paranoid but i've caught many cars on fire during fill up of the trans when the fluid burps out of the tube after a overhaul, and it is scramble time to get it out, I've had a pressure gauge blow out on me too and burned the car to the ground- I'm not fire prone, just a busy guy.