Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
Abstract Ellipses Background Grayscale
Source GDJ
Remixed from a drawing in 'Kulturgeschichte der Deutschen im Mittelalter' Franz von Loeher, 1891. The unit tile can be had by selecting the rectangle in Inkscape and using shift-alt-i
Source Firkin
Coming in at 666x666px, this is an evil big pattern, but nice and soft at the same time.
Source Atle Mo
Adapted heavily from a JPG that was uploaded to Pixabay by Viscious-Speed.
Source Firkin
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
Fabric-ish patterns are close to my heart. French Stucco to the rescue.
Source Christopher Buecheler
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Prismatic Rounded Squares Grid 3 No Background
Source GDJ
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
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 pattern recreated from an image on Pixabay. It is reminiscent of parquet flooring and is formed from a square tile, which can be recovered in Inkscape by selecting the ungrouped rectangle and using shift-alt-I together.
Source Firkin
More carbon fiber for your collections. This time in white or semi-dark gray.
Source Badhon Ebrahim
Dark squares with some virus-looking dots in the grid.
Source Hugo Loning
A seamless pattern with wide vertical stripes colored in pale yellow.
Source V. Hartikainen
Prismatic Curved Diamond Pattern 5 No Background
Source GDJ
Light and tiny, just the way you like it.
Source Rohit Arun Rao
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
Remixed from a drawing in 'Paul's Sister', Frances Peard, 1889.
Source Firkin
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.
Source V. Hartikainen
One more sharp little tile for you. Subtle circles this time.
Source Blunia