Don't bother trying to get timing down where you click as your friend starts skinning. One of you skin and not loot the leather. Then the other one does the same. Last skinner in group can collect the leather. All of you will get the chance for skill up. My wife and I found this out while running around on some alts. As mentioned above, this is the same thing you can do for mining and herbalism.
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Yes I'm still a leecher, maybe the oldest one still around.