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
Prismatic Abstract Geometric Background 4 No Black
Source GDJ
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
Original minus the background
Source Firkin
A seamless chequerboard pattern formed from a tile that can be had in Inkscape by selecting the rectangle and using shift+alt+i. Alternative colour scheme.
Source Firkin
One more sharp little tile for you. Subtle circles this time.
Source Blunia
This one is something special. I’d call it a flat pattern, too. Very well done, sir!
Source GetDiscount
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Tiny little fibers making a soft and sweet look.
Source Badhon Ebrahim
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Dark wooden pattern, given the subtle treatment. based on texture from Cloaks.
Nice little grid. Would work great as a base on top of some other patterns.
Source Arno Gregorian
Light gray version of the Binding pattern that looks a bit like fabric.
Source Newbury
This is so subtle I hope you can see it! Tweak at will.
Source Alexandre Naud
The image depicts a seamless pattern of a fishnet with a plenty of fish.It may be a lucky charm for fishermen.
Source Yamachem
Same as the black version, but now in shades of gray. Very subtle and fine grained.
Source Atle Mo
A dark metallic background with a pattern of stamped dots. Here's a dark "metallic" background pattern for you.
Source V. Hartikainen
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
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin
Black brick wall pattern. Brick your site up!
Source Alex Parker
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin