arne jacobsen egg chair  

Well...
for starters, it's not an arne Jacobsen Egg chair.
It's a vinyl 1960s/ 70s swivel armchair.

definitely leather
I'm told

Sorry
yes, looking at the magnified pictures and the stitching it could be leather.
However, it's not an Arne Jacobsen design.

thanks
any thoughts on any origins - Danish? - one off?- Commercial?

Overman?
Swedish, domestic, mass produced. At a guess.

leather or vinyl
Wave a lighter (lit) near your piece; if it smells like burning plastic, it's vinyl.

.
That won't work, invite a vegan to sit on it, if they burst into flames then it's leather.