Does it really matter if a Mud flap is made from Leather or something else?

It matters to the cow.

(Just Kidding)

I think good quality leather should last as long or longer than cheap quality plastic or rubber. Also, leather tends to be softer and more pliable than hard plastics, although the mudflap I made from an old yoga mat is very leather-like,

Leather mud flaps would nice a nice touch if your bike had a leather seat, more so if you had leather wrapped bars, and especially so if you had a whole retro/organic theme with a leather seat and leather wrapped bars, plus cork hand-grips and metal fenders.

I think the main issue is pliability so that the mudflap doesn't break, or break the fenders when encountering an obstacle.

Be creative, make your own mud flap. (And have fun ;-)

Plastic from a large motor oil bottle, available in assorted colors. I use black to match the fender. Weighs nothing, extremely strong, will not degrade or decay. The "edge" part of the bottle already has a curvature to it, which may make it a better fit to your fender. Affix to fender by drilling small holes and using small zip ties.

I'm going to attempt to make my own mudflap out of a plastic bottle and an old black leather jacket (for the material) I'm going to sew the leather to the plastic and also use the leather for a chainstay protector. Love making things! Will post pics.

I made mine from a rubber stair tread, used cable ties to attach it. That was seven years ago.

I made mine from rubber roofing (EPDM), which is extremely flexible & durable. On the bottom, I put some weights (screws + nuts) to keep it down in the wind. Works like a charm.
Be careful with zip ties....if not UV resistant, they'll break in a year or so. Wire lasts forever.

Mine are duct tape. Works for me.

No, (other than Bling Factor) stiff LDPE, is fine..