In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
Remixed from a drawing that was uploaded to Pixabay by DavidZydd
Source Firkin
Not a flat you live inside, like in the UK – but a flat piece of cardboard.
Source Appleshadow
Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
There are many carbon patterns, but this one is tiny.
Source Designova
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Prismatic Polyskelion Pattern No Background
Source GDJ
From a drawing in 'Handbook of the excursions proposed to be made by the Lincoln Diocesan Architectural Society, on the 27th and 28th of May, 1857', Edward Trollope, 1857.
Source Firkin
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Small dots with minor circles spread across to form a nice mosaic.
Source John Burks
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
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
Luxurious looking pattern (for a T-shirt maybe?) with a hint of green.
Source Simon Meek
From a drawing in 'Jardyne's Wife', Charles Wills, 1891.
Source Firkin
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Danmarks Riges Historie af J. Steenstrup, Kr. Erslev, A. Heise, V. Mollerup, J. A. Fridericia, E. Holm, A. D. Jørgensen', 1897.
Source Firkin
Prismatic Groovy Concentric Background 4 No Black
Source GDJ
This ladies and gentlemen, is texturetastic! Love it.
Source Adam Pickering
Colourful background achieved with gradient fills.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett