If the fuel filter is on the firewall you need some rubber hose between it and the motor. Between the fuel pump and the carb(s) you are better off using 1/14". If you have twin carbs a 1/4" compression tee fitting works nice and is dismantleable. So you just need to get from the fuel filter to the pump. the change from 5/16 to 1/4 happening somewhere along the way.
Unless this is a full race bonneville car, 1/4" is plenty for a flathead.
I have a similar setup on my roadster and do have a short piece of 5/16 going into the pump. A rubber hose connects to this from the firewall. As I said above, I have 1/4" between the pump and carbs with a Tee in the middle.
Nice and easy lemon squeezy, and only one 5/16 adaption to make.
Mart.