Green Fibers@2X #92
 Dark  CC BY-SA 3.0

The green fibers pattern will work very well in grayscale as well.

Source Matteo Di Capua

 More Textures
Grilled Noise #581
 Fabric  CC BY-SA 3.0

You could get a bit dizzy from this one, but it might come in handy.

Source Dertig Media

Fabric pattern 2 (colour 4) #2393
 Fabric  CC 0

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

edo pattern-samekomon #2271
 Dark  CC 0

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

Checkered Pattern@2X #323
 Grid  CC BY-SA 3.0

Simple gray checkered lines, in light tones.

Source Radosław Rzepecki

Abstract Tiled Background Extended 8 #519
 Noise  CC 0

Abstract Tiled Background Extended 8

Source GDJ

Background pattern 232 #2297
 Dark  CC 0

Heavily remixed from a drawing in 'Barbara Leybourne; a story of eighty years ago', Sarah Hamer, 1889.

Source Firkin

Heart and rose pattern #2419
 Pink  CC 0

Seamless pattern formed from a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.

Source Firkin