Vintage Tulip chairs turning yellow  

The coating is nylon.
There's a method for removing yellowing from ABS plastic that might work on nylon, too, if the yellowing happens for the same reason (brominated flame retardants) -- it involves soaking in a strong solution of hydrogen peroxide with maybe some OxiClean mixed in.
Search the web for "Retr0Bright" and read the web pages you find; they will tell you all about safe handling of hydrogen peroxide, where to buy 12% or stronger H2O2, how to apply it, how long to leave it on, etc. The link I've attached below seems to explain it all pretty well.
Maybe you'll find a web page that says for sure whether the method works on nylon as well as ABS.
Some tips: UV is your friend, but heat is not. Watch the reaction and do not let the peroxide solution dry on your chair base.
Please wear gloves and eye protection. Hydrogen peroxide is dangerous at high concentrations.
Also, do not use chlorine bleach without testing it on a small area first. On ABS, chlorine bleach won't whiten the plastic and in fact usually makes the stain worse.
And if all else fails, you can always just paint the bases.
http://www.exisle.net/mb/index.php?/topic/59657-de-yellowing-plastic-the...

For what it's worth,
I'm pretty sure chlorine bleach will turn nylon yellowish, too.