My first and simple approach was to screen-record a fluid simulation toy (there's plenty on the internet) and apply a blur and a color-ramp. The effect is OK but it's limited as it cannot create blobs of color "floating on their own", they are always tied to the intensity of the original image.
I've also tried the Texture Synthesis add-on's style transfer feature, but it doesn't really work. Another option would be procedural texture nodes. I.E. distorted texture coordinates to alter a colored image or just animated noise textures with a color-ramp on their own. However, these techniques may be limited in some ways (the distorted image will get blurry and using a color ramp would have the same problems as before).
Finally, there could be a way to do that with particles, turbolence and dynamic painting, but I'm not very confident with particles in blender.