I'm curious what tools or process you need to not only create this nice dither/dot pattern but to make it with multicolored like the example below. Thanks!
Since you are looking for a tool, I'd like to suggest GIMP because it's free, Open Source, and cross-platform. You could also do the same in Photoshop (but it's not free).
Create your artwork in GIMP (or Photshop) using as many layers as you want. I used the Pen tool to create nice smooth selections, and filled them with basic flat colours. Using a large soft edge brush set to low opacity, set the alpha lock (Photoshop: transparency lock) on each layer, and paint in some nice colour gradients, then finally add a 50% grey filled layer at the top, and do Filters > Noise > RGB Noise (Photoshop: Filter > Add noise, uncheck "monochromatic").
Set the layer blending mode of the RGB noise layer to Overlay