Clone stamp on multiple layers

It does work, IMO.

This action is safe to run. It makes a dupe and makes some layers.

It takes a sample from the orange top layer and clones it to two layers below it (then restores initial view — "fancy stuff" that is not really needed. Hiding layers isn't either.).

It's just a proof of concept. Do it how you like.

I recorded this with the ruler set to percentage, which may be essential.

If you want a specific blend mode for the Clone Tool, maybe you need to record a Clone Tool Preset that you record when selecting it. I may have forgotten other things.

Oh, you need Tool Recording to be selected (if you can't, remove ScriptListener plugin).

As often when making actions, I discover bugs galore.

I initially had three layers to clone the sample into, but by the third layer the sample somehow got lost. I also saw weird stuff where my Clone tool disappeared behind parts of the picture somehow. OTOH, I'm not the most experienced guy with the Clone Tool...

Duh, I forget how you have to attach an action, and nothing is working. Forum suck is strong with this one... 😉

Visually, the example looks like this ...

Another possibility would be to make a Path, and stroke it with the Clone Stamp tool on each layer.

By now I wonder what the OP is really trying to achieve … I suspected the problem to be something like a stack of photographs that feature the same sensor dust (or similar) but the issue may indeed be completely different.

You can't change pixels on multiple layers at once using any method... You can use the clone stamp to sample from multiple layers

Not really at once, but maybe clone to a separate layer, and then make merged copies with the rest of the layers.

Camera Raw’s Spot Removal tool might provide a solution (less than elegant though it may be), for example using the Camera Raw Filter (preferably as a Smart Filter naturally).