1/4" shanks should be fine. Question is, why are you using 3/8" ID vinyl line? If you are using 100% CO2, you must maintain temperature 24/7 at the keg and all the way to the shank while appying the correct pressure based on carbonation level of the beer and this temperature (38F). Possibly this may be 14 PSIG.
If your vertical distance for gravity is 12' from the bottom of the keg to the faucet, this equates to 6 lbs. restriction. Since you may be propelling the keg with 14 PSIG, you still need 8 lbs. in the beer tubing between the keg and shank to balance PSIG and restriction pressure in the system. This will provide approx. 128 oz / min. flow rate.
Suppose this line length required is estimated at 18'. You could use a combination of 14' of 1/4" ID barrier tubing from the shank to a splicer connected to 4' of 1/4" ID vinyl at the keg for flexibility to tap multiple kegs. For a slightly slower flow rate, add a foot to the vinyl.
Remember, if you cannot sustain temperature with correct PSIG to the keg, you will end up with a wasteful system. So much waste that you probably could have originally purchased a glycol system and gas blender twice over.
Scott Zuhse, Instructor
Micro Matic Dispense Institute