I've researched this costume quite a bit at both FIDM in Los Angeles, CIV, and even speaking with people who have examined the costume in person at the Lucasfilm archives.
The accurate cloak fabric is not easy to find (I have not come across it). It's reportedly a very thin wool. So thin in fact, someone who examined the cloak at the archives said they actually doubled up the layers for the film used costume to make it less transparent!
The outer tunic/obi/scarf like tabard I believe is a very heavy slubby silk. I didn't feel it, but a friend who is very familiar with fibers felt it and said it did feel like raw silk as opposed to linen.
Info I documented a few years ago (with modern edits)
Sources for outer tunic fabric
1) Sold by a distributor called
Stylecrest Fabrics Ltd.. It is called "Native Pure Silk - Casablanca" The closest color was Sable, but it's just a touch more brownish than the real vest. I think it could be overdyed in a weak solution of black acid dye and it would be a nearly perfect off-black. The black they sold was a bit darker than the real costume. But another idea is washing the heck out of the black and perhaps adding a touch of bleach to help fade it. (always test first!) (I now tend to lean on thinking it would be easier to buy the black and wash it... maybe enzyme wash - to fade it).
There is a chance this company may only sell wholesale to people with a resale license, I'm not sure.
Here is a scan of their silk in the sable color next to a close-up of Luke's vest from C4
2) Silk sold by
B. Black and sons in Los Angeles (it is not shown on their web site). They do not require a reseller license and will sell to the public. I call them often to order fabrics after I swatch things on trips to LA (since they don't show all their fabrics online - they can easily sell to you over the phone if you have the item number) It is called "Hand Woven Silk" by Kings Road Imports. Style 269. Either the light brown could potentially be overdyed with some black dye or the black might be able to be faded.
I'm so new here - I have yet to read up on rules about posting potential sellers/makers. I have a friend who makes the outer tunic... but last I saw she was using the brown Casablanca fabric without dying it and it looks too brown. Her pattern is pretty accurate though and she's a professional fashion designer so all her garments are well made. She makes cloaks as well, but I'm not sure if she's made an accurate Luke cloak.... yet
PM me if you want her contact info. She goes by SiaLan Wezz at the Rebel Legion. Also has a store that goes by Eva-Vanecek-Reproductions