This one is something special. I’d call it a flat pattern, too. Very well done, sir!
Source GetDiscount
The original enhanced with one of Inkscapes's filters.
Source Firkin
Tweed is back in style – you heard it here first. Also, the @2X version here is great!
Source Simon Leo
Zero CC tileable wood texture, made by me procedurally in Neo Texture Edit.
Source Sojan Janso
Prismatic Abstract Line Art Pattern Background
Source GDJ
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
A version without colours blended together to give a different look.
Source Firkin
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
Prismatic Curved Diamond Pattern 4 No Background
Source GDJ
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Bright Multicolored Floral Background by Karen Arnold from PDP.
Source GDJ
This was formed by distorting an image of a background on Pixabay.
Source Firkin
A seamless background of warped stripes on paper.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Super simple but very nice indeed. Gray with vertical stripes.
Source Merrin Macleod
Can never have too many knitting patterns, especially as nice as this.
Source Victoria Spahn
Vector version of a png that was uploaded to Pixabay by pencilparker
Source Firkin
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
A slightly more textured pattern, medium gray. A bit like a potato sack?
Source Bilal Ketab
The basic shapes never get old. Simple triangle pattern.
Source Atle Mo
Black And White Floral Pattern Background Inverse
Source GDJ