I’ve also coloured a few of the colouring book pages in Photoshop, mostly for my own amusement.
To create this effect of being printed on brown paper:
Auto trace your artwork to a black outline and transparent background on Illustrator (turn on ignore white on auto trace)
Open up the file in Photoshop
Add a scan of brown paper to the bottom layer
Set the image outline layer to multiply mode and then copy the layer so it’s doubled up, and the topmost layer
Use a separate multiply or hard light (whichever works better for that colour) layer for each colour underneath the outline, and colour in blocks using the most basic paintbrush (not one with airbrushing- the blockiest kind). Adjust the opacity of each layer to strike a balance between colour density and letting the paper texture show through.
You can also use add noise and colour halftone filters on the colour layers to add texture- the roof here is one plain colour layer and one halftoned layer.