Identification & advice re restoring old oak rocking chair  

Your photos are tiny, so there isn't much to say based on them.

Stylistically, I would guess it might be an American Arts & Crafts Movement piece.

The through tenons are very Craftsman style but all that tapering and rounding of edges going on looks more Scandinavian to me. The way the back is meant to be upholstered---that's more an American Victorian style! And maybe English, too, not sure. As far as style, that's all I've got.

There are lots of instructions online for upholstering open back chairs---some good, some bad. This video series is pretty good:

https://www.youtube.com/watch?v=ZCe7MBJNXgc

Do you have any upholstery experience? This is not really a beginner project but if you are the careful, meticulous type and are good with your hands, you can probably swing it. Having the right tools is very important, too. It will be much easier to do with a pneumatic stapler like that guy is using. The tacking surfaces are very narrow in a chair like this and it takes a lot of practice to tack neatly and accurately, and an electric staple gun uses heavier gauge staples that can end up splitting the wood (plus they tend not to go into the wood all the way and need hammering in to complete the job).

I can't really tell if this is even how the back on yours is done. You really need to strip out all the old fabric and webbing (if there's any webbing!) and see how the frame is constructed. It looks like there is some tacking done from the back in that one straight-on back view. That would be different from the chair in the video that I linked.

The seat is probably meant to be done sort of like the back but maybe with a loose cushion on top for more comfort. Also hard to say without seeing the frame and better detail shots.

The construction may also require double welt or gimp around the edges of the fabric in the inside back, to cover the staples---this is a particularly fussy job.

You may be tempted to just cut plywood inserts for seat or back or both, but try not to give in to this. Webbing is way more comfortable. And you do need webbing as the weight of the human body sitting in the chair will eventually stretch out most upholstery fabric and could also cause it to tear away at the staples. The webbing is the foundation.

Please don't hesitate to ask more questions as you proceed! Now I'm curious about the way the back frame is made, like where the tacking surfaces are.

Oh, and I would just go with a good Danish upholstery wool in a solid(ish) color, to bring out that look in the kind of schizo frame style. Fortunately you won't need much fabric at all, so shopping for discounted remnants online is an option.

I appreciate your thoughts.

"Schizo frame style" seems to fit as it doesn't have the heft that is more typical of arts & crafts style but I'm hearing from you that the through tenon construct is mostly a hallmark of Craftsman. And the open back is typical of American Victorian or English...

This reupholstery job sounds a tiny bit more complicated that I was hoping but I will check out youtube you suggested before talking myself out of it. I may be poorly suited to this particular challenge as I am both inexperienced at upholstering anything beyond cushions AND not particularly patient. On the plus side, I like things to be done right and I enjoy seeing interesting items restored to their more authentic/original condition.

Which with this chair, I guess will be restoring it to its original "Craftsman-Scandinavian-American Victorian" roots.

So very American.

I'll post photos of the frame after the fabric is removed.

El