Can't tell without a picture.

Sorry. I’m trying to post the photos but unfortunately Houzz is not showing them in the posting :-/

Hadn't thought about those in years. My grandparents had a couple like that on the porch in the 1940's....that's all I know!

Style looks to be early 20th century, but I haven't seen any folding rocking chairs like that before. Folding chairs yes, but rocking? One must ask oneself why folding, to gain a direction. Two main possiblilities (but could be others): 19th and early 20thC people were on the move a lot more so, one: possibly off a boat/steamship, a deck chair (not a deck-chair) designed to be folded away and stowed when not in use. Two, During those periods, military personnel (officers) would have furniture made to specification (see Campaign Furniture) to be easily packed and transported over great distances and quite often difficult terrain on mules. All designed for easy packing and easy assembly at destination.

Hope this gives you a start to finding the origin.