The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Prismatic Polka Dots Mark II 3 No Background
Source GDJ
Derived from an image that was uploaded to Pixabay by TheDigitalArtist
Source Firkin
Zero CC asphalt, pavement, texture, photographed and made by me. CC0 WARNING I FOUND A SEAM ON THIS TEXTURE
Source Sojan Janso
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
Three shades of gray makes this pattern look like a small carbon fiber surface. Great readability even for small fonts.
Source Atle Mo
From a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.
Source Firkin
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
Imagine you zoomed in 1000X on some fabric. But then it turned out to be a skeleton!
Source Angelica
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
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
This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen
Super simple but very nice indeed. Gray with vertical stripes.
Source Merrin Macleod
A comeback for you: the popular Escheresque, now in black.
Source Patten
Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i
Source Firkin
Number five from the same submitter, makes my job easy.
Source Dima Shiper
Inspired by a 1930s wallpaper pattern I saw on TV.
Source Firkin
The act or state of corrugating or of being corrugated, a wrinkle; fold; furrow; ridge.
Source Anna Litvinuk
The image depicts an edo-era pattern called "same-komon" or "鮫小紋"which looks like a shark skin.The "same" in Japanese means shark in English.
Source Yamachem
Number 3 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
Prismatic Snowflakes Pattern 2 No Background
Source GDJ
A repeating background of thick textured paper. Actually, it turned out to look like something between a paper and fabric.
Source V. Hartikainen
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba