This one is something special. I’d call it a flat pattern, too. Very well done, sir!
Source GetDiscount
You know you can’t get enough of these linen-fabric-y patterns.
Source James Basoo
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Prismatic Groovy Concentric Background 5
Source GDJ
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A seamless pattern the starting point for which was a 'rainbow twist' texture in Paint.net.
Source Firkin
Zero CC tileable brick texture, photographed and made by me. CC0
Source Sojan Janso
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
Based on an image that was uploaded to Pixabay by devanath
Source Firkin
This one is amazing, truly original. Go use it!
Source Viahorizon
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
A dark metal plate with an embossed grid pattern and a bit of rust. Here's a dark metal plate texture for use as a tiled background on web pages.
Source V. Hartikainen
Love me some light mesh on a Monday. Sharp.
Source Wilmotte Bastien
Pixel by pixel, sharp and clean. Very light pattern with clear lines.
Source M.Ashok
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A seamless pattern formed from a tile made from ornament 22. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin