You can use a photo of a texture, there are sites online to download them. https://duckduckgo.com/?q=texture+images
You also could paint something phisically, and take a picture of it.
Convert it to grayscale.
Change the mode now to duotone, actually you need a monotone, just use only one ink on the dialog box.
Play with the blending modes, probably use multiply for start.
You can also play with the contrast of the image, to make things more transparent slide the white side.
There is a chance the images are also skewed or distorted a bit.
The section with the blue sky could be an additional rectangle with cyan color in it.