Which Straps on this type of Selig slot?  

Pirelli rubber fagas straps (or the contemporary black stretch webbing for seating) with metal clips at the ends.  There are two types of clips: 45 degree and 90 degree.  Which you need depends on the slot on the chair.  Last time I replaced some clips (non-selig chair) I could only find 90 degree clips and needed 45 degree one.  So I just bent them with a pliers.  

http://www.fagasstraps.com/clips.asp
Evans is now selling these patented 45 degree clips for use with Pirelli straps, for making your own straps to custom lengths.  I was told by someone who recently spoke with Evans that they will be phasing out the sale of Fagas straps in the USA, and I believe their offerings of Fagas straps is already very limited in terms of the sizes available.  The new Evans clips are not exactly cheap, but I have been told they work well with Pirelli strap material.

Does anyone have an opinion as to Pirelli or webbing? I don't mind spending the money on Pirelli if it lasts longer. I do live in a dry climate. Will the rubber dry out faster?Can you put more than the 3 straps across each way if you want firmer support?
Regarding the phasing out of sales...guess this means we should all stock up? Will we be able to order them from overseas?

Good prices here for both Elasbelt (the black elasic strap with red stripe), as well as the 45 degree clips. Less expensive for the more you buy.
 
I've used them for replacement on this same Selig groove slot and they work very well. I'm not sure about lifespan comparison between Pirelli and Fagas, but for me the performance/cost ratio gives the edge to Elasbelt.
 
http://www.diyupholsterysupply.com/Upholstery-webbing.html  

The grooves on some chairs are very narrow and on others are quite wide.  I have the webbing described by cdsilva above and also got clips to crimp on to the ends.  I got them for a chair that I had years ago and was dismayed to find that even when crimped as flat as possible, the clips still wouldn't go into the grooves.  
On the other hand, I used them on a Kofod-Larsen recliner recently and they were a perfect fit to the grooves---very snug, no danager of popping out.

Spanky-Do you think it is the webbing or the clips themselves too thick? Were you trying to put them into a Selig? The slots on my chair look narrow, but guessing that since the Evans clips are made for the Selig chair, they will be ok?

I just spoke with Evans. They are fading out the Fagas because their product is better for less money. The quality of Fagas straps was declining while the costs were skyrocketing. The new product is about $3 a strap cheaper and lasts 3x as long. The Evans Clips are an improvement on Fagas.
To all-I myself am extremely happy I can order clips that work for my chair. Be happy that someone has taken the time to design and manufacture these for us. I won't bemoan paying a few bucks for products that help me restore my chair to a useable state.

H all, great discussion!
At Evans Company, we have designed and manufactured our 45-degree Evans Clips in Scandinavia as an improvement and replacement to the Fagas Strap. Our Evans Clips are made in galvanized steel and stone tumbled so they last and won't harm your furniture. The Fagas Straps sadly have been declining over the years in quality and therefore longevity, and to top it off, the cost was dramatically increasing every year! We thought we'd do our part to continue to provide customers with quality replacement straps, while not passing along the cost, so we developed the Evans Clip. When purchased along with your choice of webbing (we sell Pirelli and Poly webbing), Evans Clips straps are dollars cheaper per strap than Fagas Straps.
Evans Clips are made to be used with 45-degree angle slots, commonly found on Selig chairs and sofas, but are on many types of mid-century furniture. Forty-five degree slots are narrower than 90-degree slots, and therefore 90-degree metal grips, being thicker than Evans Clips, will not work. We do sell the 90-degree grips for furniture with thicker, 90-degree angle slots. 
To install Evans Clip straps, the length of your straps will depend on which type of webbing you choose. Pirelli webbing should be cut 1/2" sorter than the slot-to-slot distance. Evans Clips are to be clamped onto each end of the webbing using a pliers, BUT BE SURE NOT TO CLAMP THE 45-DEGREE FLAPS, AS THOSE ARE WHAT HOOK INTO THE SLOTS. If you're using Poly webbing (which stretches more), cut the webbing 1- 1 1/2" shorter than the slot-to-slot distance.
Vsit our website: www.fagasstraps.com for more info, or feel free to email us directly: info@fagasstraps.com. Thanks!! -Jon

Thanks for contributing Jon.
It's a blessing to have a company that designed and manufactured a clip to fit my chair so I don't have to go searching for half baked solutions. Worth every penny imho. And I know it costs money to design, machine and bring items to market. Lots of companies won't bother to design things they can't sell in the billions.Thanks so much for providing these for purchase and serving the smallish market of mid century collectors. Good information about the 90 degree clips being too thick for the 45 degree angle slots. Learn something new here every day.

For the record, I don't think it's as simple as thick clips being for right angle slots and thin clips being for 45 degree angled slots.  The wider slots on the Kofod-Larsen chair that I did recently were angled.  

Interesting. Post pictures if you get around to it. Thanks Spanky.

I already delivered the chair I was talking about above but I have another that might have the wider slots.  It may be awhile before I can dig it out and check, though.

I'd like to see as well.To all, got this task done. I am amazed how easy it was. I don't know why I stressed about it. Took me about twenty minutes. The Evans Clips worked really well for me. But I'd love to see your chair Spanky so I know how to solve the problem in case I come across it.