You could achive that effect with slight colour shifts and a very low opacity spray/wash/sponge, but I think your best bet is probably use a pattern or a canvas texture.
There are some default textures which are explained here:
https://www.davidrevoy.com/article156/texture-pack-1
and this thread suggests using procreate textures:
https://krita-artists.org/t/20-free-paper-canvas-textures/77155