The yarn used for the sample design is Allegoro by Classic Elite Yarns. It is a loosely plied 70% cotton, 30% linen and it's about 6 st. to the inch in gauge with size 5 US needles. This guide
puts at about a sport to DK weight. It's a fairly new pattern so there isn't a lot of info about it yet even on Ravelry.
I don't know of specific yarns, but I know bamboo produces a drapey fabric so it might be an option. Hopefully someone else here can help you out with info.