I looooove linen! Great for summer. I haven't made a wrap myself, but Jan at SBP has a
good FAQ on fabric for slings. Even though she's talking about ring slings, which obviously have to take a lot of stress at the seam/rings, some of the info is good to keep in mind for a wrap too (ie, not using super lightweight/handkerchief fabrics, or quilting fabrics), and there's a list of online fabric stores

I don't know what the prices are like on Etsy, but if you have a sewing machine hemming a wrap is really easy to do so you might save some money buying enough fabric for 2 or 3 wraps and doing it yourself.
I know several mamas have made DIY linen wraps from blends and from 100% linen fabrics and they are quite happy with them. Osnaburg is another great choice than many people use to make wraps, but it's not linen (100% cotton).