Apply Fractal Noise to a solid layer, animate the Brightness and Contrast to begin at white and end with a black plate, animate the evolution.
Precomp the noise layer.
Use that as a luma matte on the layer you want to burn.
You can reuse the fractal noise comp beneath the burning layer and apply Colorama and a glow.
This sample is a bit lame but it took 2 minutes to make…
Luma Matte