Stainless steel braided line
I would recommend using the nickle copper line you mentioned to the bracket where the rubber line would clip in and then use either ss braid from there to the wheel cylinders or OEM rubber. Nickle copper bends super easy and will not kink. You can purchase a tubing straightener from Eastwood or similar supplier for the straight portions. I first learned about nickle copper when I was standing at the order desk at Brake Equipment Warehouse in Minneapolis, Mn a few years ago. There was this 6" piece laying there...I picked it up and the sales guy says "kink it!". I tried and tried and could not. The most amazing thing is that it does not work harden but stays soft. "That piece has been bent back and forth for 2 weeks", he said. I ended up walking out with a spool of the stuff.
Another means of straightening tubing is to put a little pull on it. I used to train power plant mechanics for a large utility. We would straighten very long lengths of tubing of all sizes that way. The important consideration is wall thickness as you do not want to thin it out. Swaglok company has charts with wall specifications but if you only put a little pull on it, you will be fine. If anyone is interested, I can sketch a drawing of a homemade stretching tool we used for short lengths. For long lengths we used comealongs.