Here's the dissolve portion.
dropbox.com/scl/fi/4xlpja8hk97ttb9lwvlm4/dissolveexample.c3p
It involves using a noise texture from the advanced random plugin on a drawing canvas, placed above the target sprite on a layer with force own texture enabled, setting the blend mode to destination in, and using an alpha clamp effect with the threshold tweened from 0 to 100%.
Set the blend mode of the drawing canvas to normal if you need help to visualize what's happening. You can also use the destination out blend mode instead, and tween the alpha clamp threshold from 100 to 0 instead for more or less the same result.
For the fire part, I imagine you would do exactly the same thing, using the same noise pattern, on a fiery colored texture, but timed so that it starts slightly ahead of the dissolving part.
The linked effect uses simplex noise instead of perlin noise, but perlin is what we have to work with here in the advanced random plugin, short of importing the simplex algorithm manually or through a JS library.