A simple example on using clones. You can generate a nice base for a pattern fill quickly with it.
Source Lazur URH
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
A seamless tessellation pattern. To get the tile this is formed from, select the pattern in Inkscape and use shift+alt+i.
Source Firkin
Inspired by a drawing in 'Kulturgeschichte', Freidrich Hellwald, 1896.
Source Firkin
This background texture resembles stone. It may be used as a background on web pages or on some of their html elements (header, borders, menu bar, etc.). Just modify it for your needs.
Source V. Hartikainen
I’m starting to think I have a concrete wall fetish.
Source Atle Mo
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I. Version with black background.
Source Firkin
A dark gray, sandy pattern with small light dots, and some angled strokes.
Source Atle Mo
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
After 1 comes 2, same but different. You get the idea.
Source Hendrik Lammers
With a name this awesome, how can I go wrong?
Source Nikolay Boltachev
Same as Silver Scales, but in black. Turn your site into a dragon with this great scale pattern.
Source Alex Parker
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
Derived from an image that was uploaded to Pixabay by mdmelo.
Source Firkin
This tiled background comes in red and consists of tiles that look like gemstones. It is more for blogs or social profiles, I think.
Source V. Hartikainen
Remixed from a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892. The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Derived from a drawing in 'Historiske Afhandlinger', Adolf Jorgensen, 1898.
Source Firkin
On a large canvas you can see it tiling, but used on smaller areas, it’s beautiful.
Source Paul Phönixweiß
CC0 and seamless wellington boot pattern.
Source SliverKnight
To get the repeating unit, select the rectangle in Inkscape and use shift+alt+i
Source Firkin
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