Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
White fabric looking texture with some nice random wave features.
Source Hendrik Lammers
Beautiful dark noise pattern with some dust and grunge.
Source Vincent Klaiber
Dark, crisp and subtle. Tiny black lines on top of some noise.
Source Wilmotte Bastien
Super dark, crisp and detailed. And a Kill Bill reference.
Source Badhon Ebrahim
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Hexagonal dark 3D pattern. What more can you ask for?
Source Norbert Levajsics
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Could be paper, could be a Polaroid frame – up to you!
Source Chaos
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
A gray background pattern with a texture of textile. Suits perfectly for web design.
Source V. Hartikainen
Dark Tile-able Grunge Texture. I think this texture can be classified as grunge. It's free and seamless, as always.
Source V. Hartikainen
A lovely light gray pattern with stripes and a dash of noise.
Source V. Hartikainen
Sharp diamond pattern. A small 24x18px tile.
Source Tom Neal
Carbon fiber is never out of fashion, so here is one more style for you.
Source Alfred Lee
Semi-light fabric pattern made out of random pixels in shades of gray.
Source Atle Mo
A pattern derived from repeating unit cells each derived from part of a fractal rendering in paint.net.
Source Firkin
From a drawing in 'Navigations de Alouys de Cademoste.-La Navigation du Capitaine Pierre Sintre', Alvise da ca da Mosto, 1895.
Source Firkin
Not the Rebel alliance, but a dark textured pattern.
Source Hendrik Lammers
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
Remixed from a drawing in 'A Girl in Ten Thousand', Elizabeth Meade, 1896.
Source Firkin