I have 2 sets of wheel both are 5.25 BS. With 31" tires would the rubbing on the LCA be reduced if I were to put the on my 15x8 Canyons? They are now mounted on 15x7 steelies and rub the LCA.

 

I would think that since they both have 5.25" backspacing they would rub the same.
I have the 265/75R16 (~31.6") on my stock rims 16x7 and i believe the backspacing is 5.25" and my tires rub on the LCA when im at full lock.
You want to push the tire out a bit so it won't rub so you would need a rim with less backspacing.

 

don't matter what rims. same backspacing

 

Thats what I was thinking. The wider wheel might make the side wall with a little narrower, but the tread width wouldn't be changing. The center of the tread would move out ward a little, but not enoughto make much difference.