Mrs. S was very fortunate to have in her stash a hunk of linen ready to be cut out into a shift. Most of us have to go shopping! Finding the right linen for a shift is not that difficult.
Our regular suppliers are a great place to start.
Follow the link, this is the linen that I would choose for a shift from Burnley and Trowbridge.
The 3.7 oz linen is a good choice from Wm Booth Draper.
The main chain store remaining to us, Jo-Anns Fabrics, also carries linen, but the selection is limited.
Still and always some of the best linens come from Ireland and Ulster Linen sells many weights and varieties. The down side is the cost, the linen is expensive, and there is a 30 yard minimum order to avoid a cutting fee. If an entire unit or group were to do an order, that would be achievable.
Online the best place to shop for linen is the Fabrics Store. Avoid the softened linen if you can, it has been processed and is not as crisp as regular linens.
My personal preference is for the lightest finest linen that I can find, my skin is very unhappy with coarse fabrics. The weight and quality of the linen you buy and use for your shift should reflect the persona you portray. A poor camp follower would have coarse, sometimes even unbleached (brown) linen for her shift. A Boston fine lady would have a much finer, lighter linen for under her silk gowns, so keep that in mind when shopping.