recommendations for flokati, alpaca, etc?  

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Long pile mohair? I just wonder what this sort of fabric would look like after having been sat on - I wonder if it might just be flat and matted. I am no designer, but I'm not sure if this sort of fabric would make a good seat covering in practical use. I hope you find what you're looking for though.

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Long haired goat? Or Camel? Alpaca? I just did some searching and always though mohair was camel.

synthetic?
Synthetic?

That actually does look like...
That actually does look like fake fur. You can get some pretty nice fake fur these days but it isn't cheap.
You could also look at Icelandic sheep hides. Icelandic sheep (raised in many places outside of Iceland) have very long wool but it usually has a slight wave to it. It comes in a range of natural colors from creamy white to gray and dark brown and maybe black. It's kind of silky and I don't think will mat up on a seat.

Yep. Fake fur.
If you want this tipped look (where the ends of the hair are a different color than the rest of it), google "faux fur". And be sure to get swatches first. The fibers of cheaper fake fur are rougher and will clump up pretty quickly and will feel unpleasant. Think cheezy old bathmat. The better stuff is hard to distinguish from real fur.
http://www.modernity.se/20th-Century-Design/ArtID/1886/Chair-Due-Piu-Des...

THANK YOU EVERYONE ! ! !
I appreciate your words, thoughts, ideas.... awesome community here.

Icelandic sheep hides are amazing!
Thanks!