The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
This one could be the shirt of a golf player. Angled lines in different thicknesses.
Source Olivier Pineda
From a drawing in 'Bond Slaves. The story of a struggle.', Isabella Varley, 1893.
Source Firkin
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
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
Paper pattern with small dust particles and 45-degree strokes.
Source Atle Mo
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
To celebrate the new feature, we need some sparkling diamonds.
Source Atle Mo
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857.
Source Firkin
Three shades of gray makes this pattern look like a small carbon fiber surface. Great readability even for small fonts.
Source Atle Mo
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett