A few random points to consider:
I should declare that my first and only foray into laminating was using bought veneers and resulted in a very heavy guitar back that, although it looked the part, was not used and eventually binned.
Most plies for plywood and veneers for wood laminates are knifed from circular logs along their circumference, and so are 'quartersawn' by default.
If the layers of a laminate are thin enough and the outer layers are quartersawn it is very difficult to pick laminates from solid wood unless the end grain is visible, so for backs (and sides) if bound, there are no visible clues.
Flatsawn laminates can show some very interesting and attractive grain patterns in circular and “S” shaped swirls. To me, this looks a bit unnatural or at least, non-traditional.
For ukulele, if you intend to do dished backs you can get away with pretty well anything as long as your bonding technique is sound.
Their is a heap of information on internet forum pages and YouTube on guitar wood laminating.
I think, that arguably, this technique has more merit for larger bodied instruments than it has for ukulele.(Personal preference only).
The main benefit is that you end up with a super-strong one piece back that many believe sounds superior.