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
It’s an egg, in the form of a pattern. This really is 2012.
Source Paul Phönixweiß
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Carbon fiber is never out of fashion, so here is one more style for you.
Source Alfred Lee
A repeating background with seamless texture of stone. There haven't been any stone-like backgrounds for a while, so I have decided to create one more. The rest can be found in the appropriate category.
Source V. Hartikainen
Luxurious looking pattern (for a T-shirt maybe?) with a hint of green.
Source Simon Meek
Carbon fiber is never out of fashion, so here is one more style for you.
Source Alfred Lee
A seamless pattern created from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
This is the remix of "blue wave-seigaiha".The image depicts a seamless pattern of the front upper part of Japanese five yen coin which is used currently.This design represents a rice with ripe golden ears.
Source Yamachem
One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
Black & white version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
A seamless design of flowers remixed from a jpg on Pixabay by Prawny.
Source Firkin
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Embossed lines and squares with subtle highlights.
Source Alex Parker
Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic
Source Firkin
To get the repeating unit, select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Farmer could be some sort of fabric pattern, with a hint of green.
Source Fabian Schultz
Seamless Prismatic Geometric Pattern With Background
Source GDJ
It looks like a polished stone surface to me. Download it for free, as always.
Source V. Hartikainen