If you want black clothes, you shear a black sheep, wash the wool, spin it into thread, weave a garment and wear it! You don't bother dyeing linen.

(I started replying to a now-deleted comment, realized that the answer might be for enough for top-level.)

Even these days black sheep are really dark brown. Maybe a few of them but I'm no sheep expert.

So, I AM a bit knowledgeable on this, not because of anything Greek, but because of something more local and slightly more recent: Navajo Weaving. While it's a different culture and time frame, the (in some cases, self-imposed) restrictions on what they had available, and looking at the results, we can see where they got their colored clothes and textiles from.

So how did the Navajos get black in their textiles? And how black was it? And can we see for ourselves what that looked like?

(Spoilers: Black sheep, very black, and yes!)

Let's get into some background here.

Within the Navajo nation, different regions have different style guidelines, so you can tell where a textile was made by how it followed those rules.

For example, weavings made from the Two Gray Hills area use no dye, and only use natural, home-spun wool; so they only have the natural colors of sheep wool; white, brown, and ... black. Gray and beige and other gradients are made by "carding together" two wools. Here's a video showing the process.

So for an example...

Here's one of my favorites. This is an absolutely beautiful weaving, and qualifies as a tapestry for having over 80 running wefts per inch. So not only is the homemade, handspun wool very thin, Mrs Ornelas' masterpiece here is nearly 2m long.

Ganado style, from the Ganado trading post, is almost the same as Two Gray Hills, except they use a specific, unique red dye that Spanish traders would sell to them.

Here's an example of a 20th century Ganado textile. also from the Heard museum collection. While commercial dyes were certainly available to them at the time, you can see the blacks are plenty dark.

So I'm picking just what the Heard Museum has here because these are color-corrected, archival photos. The blacks you see are the blacks you get.

There are other examples; I've got a Two Gray Hills on my wall and an old Teec Nos Pos (similar to Two Gray Hills, but more triangles and allows vegetable dyes) throw rug right next to me. And the natural black wool, once washed and spun, is plenty black enough.

So... that is that. Black textiles come from black sheep wool. Any culture with access to sheep -- Greek, Navajo, Scottish -- had access to black, white, brown, and variations in-between just from the sheep themselves.

Anyway. Recommend reading... Navajo Rugs: Past, Present and Future, with the revisions by the Bobbs, even if it's a bit old, for general knowledge on Navajo weaving.

And Barbara Teller Ornelas, who made that legendary Two Gray Hills above, wrote a book on the craft and History.

And finally: Navajo Weaving in the Late 20th Century by Ann Lane Hedlund, which describes not only these traditions, but how weavers began to move away from them during this period. And lots of great photos!