I would tea dye a damask tablecloth I already owned, and use burlap as sort of a runner/second layer. Several lifetimes ago, I had a cloth doll business, and tea dyed the muslin for their bodies. It's an easy process, and produced just the look I was after. There is no need to iron damask anymore. I really prefer the soft and rumpled look.
The burlap was easy to find at Jo-Anns. I cut off a long length, washed it and dried it. I am really pleased with the look! And at a cost of under $6.00 for the burlap, really pleased with the cost.
And I must give credit to the KINGS OF BURLAP, the boys of Barn House.