You didn't state if you were looking for fabric or finished clothing.
For fabrics in SF, basically look up any fabric store & go to them. You're pretty much guaranteed they'll have some. Shop around for prices - Britex is going to be lots more expensive than, say, Discount Fabrics, but they'll all carry it. SF is sorta "Burner Central" after all.
For finished clothing: try stores along Haight St, any costume store, and you can try your luck at thrift stores (if you have time to keep checking & are a common size). Pre-made fake-fur clothing isn't going to be cheap, but if you can't sew, or don't have someone who you can get to sew for you, it's a convenient way to go.
If you're confident of your sizing, just google fake-fur (or faux fur) and clothes. You'll get tons of options to choose from. Just remember custom clothing is on the expensive side.