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
We have some linen patterns here, but none that are stressed. Until now.
Source Jordan Pittman
A light gray fabric pattern with faded vertical stripes.
Source V. Hartikainen
Some dark 45 degree angles creating a nice pattern. Huge.
Source Dark Sharp Edges
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
Inspired by a pattern found in 'A General History of Hampshire, or the County of Southampton, including the Isle of Wight', Bernard Woodwood, 1861
Source Firkin
The original enhanced with some gradients.
Source Firkin
Remixed from a drawing in 'A Child of the Age', Francis Adams, 1894.
Source Firkin
Alternative colour scheme. 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
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A web texture of brown canvas. Will look great, when used in dark web designs.
Source V. Hartikainen
Prismatic Curved Diamond Pattern 5 No Background
Source GDJ
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i
Source Firkin
A repeating background of beige (or is it more vanilla yellow) textured stripes. One more background with stripes.
Source V. Hartikainen
A large pattern with funky shapes and form. An original. Sort of origami-ish.
Source Luuk van Baars
The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.
Source V. Hartikainen
Based on an image that was uploaded to Pixabay by devanath
Source Firkin