Need help ID this chair. Ib Kofod Larsen? Should be so lucky b  

I really don't think it's Ib Kofod-Larsen---not with the minimally-shaped parts and that wood species. I can't tell what the wood is but it doesn't look like teak. Most of the chair is made of parts that are flat boards all the same thickness. Furniture by well-known designers usually consists of turned parts with diameters and shapes that are intrinsically important to the piece. I don't know if that's the best way to say that---do you know what i mean, though? eta: i shouldn't say most are even of turned parts--but this looks like stock lumber parts, like costs were kept down by not having to do much beyond cutting the outline and rounding the edges, y'know?
I'm guessing the chair is American but I could be wrong. Please post some clear, well-lit shots of different parts of the wood grain. That can often help to ID the part of the world that it's from.
Cushions---mostly the question is how thick the seat should be and you can narrow it down a bit by two things. One, the chair is low so the thinner the cushion, the lower the finished seat height will be. Lounge chairs with low seat height were popular in the 50s and 60s but you also want to be able to get out of it. Look at Finn Juhl's Japan chair for reference, though it has a very different look because of the floating seat.
Two, those two front ends of the sides that stick up---i don't think you want to have the cushion lower than those. Four inches thick might look too clunky though---but in the end it's up to you. I don't think the chair is an important enough piece to worry about restoring it exactly like the original, and cushions are a totally reversible element anyway.
The thickness of the seat cushion will determine the thickness of the back cushion. It should be a little thinner, otherwise the chair will look top heavy in my opinion. Use foam that is one level softer in density than the seat. Foam of the same density in both usually makes the seat seem too soft or the back too firm.
Fabric: I would first deal with the finish on the frame, which looks dry an dull, at least in the photos. Maybe it's better in person? Once that's looking its best, I'd probably go for a higher end wool to add as much class as possible. But a fun patterned fabric would be good, too---if you plan on selling it, you should stick to neutrals, though. They appeal to the broadest market.
My go-to place for fabrics (other than my own stash, I mean) is modern-fabrics.com---lots of remnants, discounted, tons of higher end things. Super service, though they are slow to send out swatches.

Looks like birch or possibly maple, from what can be seen in the photos. Really impossible to tell without better pictures though.....

Sorry about the quality of pictures. I came up with the Larsen guess because of these pictures.

Looks like an old knock-off of that design. Very similar but with some vital elements eliminated to cut down on production costs.

And the set with the grey cushions is not the same as the armless chair designed by Kofod Larsen for Selig. It was not designed by Kofod Larsen. There is an extra dowel in that grey cushioned set. Kofod Larsen's armless chair has triangle shaped slats (common to many Selig designs) not dowels. Also note the wood plugs on the sides. Not a Selig characteristic.

Spanky, Leif, thanks for all the information. This is a learning experience for me.
A little background information. The chair was purchased at a estate sale. There were quite a few Danish and MCM pieces there.
You guys have convinced me that is not a Kofod Larsen. But I'm including a few more pictures anyway.
I replaced that strapping. It was made of rubber and was falling apart.
The slats for the chair back are flat cushion wife and triangular outside.
Also noticed that the front of the chair is upside down the holes for the seat bottom dowels are on the bottom..apparently the chair comes apart and somebody didn't do a good job
Again thanks for all the help.