Nothing beats vintage. :) I suppose really fine Egyptian cotton would work nicely. Maybe you could get a sheet made of it at a linens store that you could cut up for lots of hankies.
I've bought mine and made mine. I like making them outta cotton and adding a bit of lace trim to them. You can also sometimes get linen fabric at JoAnns.
Glad I came across this thread this morning, I've been wanting to make some more hankies! They are amazing for kids noses, well and for us big people too! Plus they are washable and kids like to shred kleenex if they happen to find the box. :)
Mothers are those wonderful people who can get up in the morning before the smell of coffee. ~Author Unknown