Suggestions for fabric for Grant Featherston R160s chairs  

It's hard to tell what that green fabric is without a closeup. It looks like a crosshatch texture in a flat weave, maybe. Lots of mills do fabrics like that---try Unika Vaev, Designtex, ArcCom, and Maharam for starters.
For a curvy chair like that you don't want anything too stiff, so avoid heavy backings and weaves that don't have any give to them. Knoll "Classic Boucle" would be very easy to work with but the colors are really limited and it's not Danish. Better would be Kvadrat "Tonus" (Maharam is the US distributor). It's a Danish wool with a bit of elastic fiber in it which makes it perfect for curvy stuff. It was used a lot on Egg and Swan chairs. It comes in a lot of beautiful colors so you should have no problem finding one you like! You can get swatches from Maharam.
Oh, and check ModernFabrics.com---they sell mill ends of beautiful MCM-appropriate fabrics and they usually have some Kvadrat wools. Their prices are below wholesale most of the time.
I'd probably do the same fabric on both chairs if they are gonna be in the same room. But there's no law that says you have to do it either way, just do what you like and what looks best in your home.

Thx Spanky for your really helpful and informative reply! Kvadrat have some beautiful fabrics 🙂