...This got me to thinking; where did the notion of flying carpets originate? I think it was an Arab tale, rather than coming from a rug producing area. ...
The trail leading back to the origins of the magic / flying carpet concept is murky, branches off in disparate directions, and inevitably leads to lore and legend from multiple cultures and traditions.
The seemingly obvious birthplace for the magic carpet concept (Arab / Muslim lore) isn't a certain, nor arguably even a dominant, contender. Early attributions of a flying carpet are made to multiple historical figures, some attributions pre-date
The Thousand and One Nights, and they aren't of Arab origin.
Magic carpets don't get much mention at all in
The Thousand and One Nights, and the particular story usually cited as the earliest reference to such carpets concerns a prince who purchased the carpet in India. This carpet was something more akin to a magic portal or apport, insofar as it delivered the owner to wherever he wished to go 'in the twinkling of an eye'.
Writer / blogger Azhar Abidi's essay 'Secret History of the Flying Carpet' focuses on manuscripts attributed to a 13th century Jewish scholar named Isaac Ben Sherira and discovered in Iran by a Frenchman named Henri Baq. This essay is accessible online at Abidi's blog:
http://secrethistoryflyingcarpet.blogspot.com
... and you can access its 2004 published form in:
Robert Dessaix (Editor),
The Best Australian Essays 2004, Melbourne: Black, Inc., 2004, pp. 132 ff.
... which can be accessed at Google Books:
https://books.google.com/books?id=q...AQ#v=onepage&q="Secet History of the"&f=false
Ben Sherira highlights Solomon (yes, that Solomon ... ) as the earliest, or one of the earliest, figure(s) to have received and used a magic carpet circa the 10th century BCE. There are two versions of the carpet's origin. One claims God gave Solomon the carpet, and the other claims the Queen of Sheba commissioned it and forwarded it to Solomon as a hopefully overwhelming gift.
As a legend from Jewish lore, Solomon's carpet is cited in
The Jewish Encyclopedia:
http://www.jewishencyclopedia.com/articles/13842-solomon#anchor14
It would appear impossible to confirm a single-point source for the magic carpet trope, or even to assign high probability to an Arab origin its historically recent fictional appearances bias us into presuming.