You could try turning the denoiser off, as it can sometimes cause this kind of flickering in animations.
Apparently overlapping physical lights can also cause some noise, so that’s another thing you could check, as well as the radius of any physical lights.
Lastly, roughness can also produce something like this, so you could tweak that a bit and see if it makes any difference.
Oh, and I would suggest lowering the pixel filter size to 1.5.
I’m not sure if it has anything to do with the problem you are facing, but the standard value of 1.5 usually works well so if there’s a possibility that it’s the cause here you could try that as well.
In the topic Joakim mentions their were clear hotspots in the emerald’s surface because it had roughness. I think in your scene you could get a better render without the denoiser like Joakim mentions.
If I’m wrong the KeyShot people should correct me, I think the noise is a pattern which changes from frame to frame. A bit like some random noise. So if you would do a denoise pass the result of every frame would also be different. And in area’s where there is quite some noise that will be noticeable.
When I had it on the background once I used the deflicker option from DaVinci which actually helped. Not sure if something like this would work since it’s such a small surface.
You could try to change the material a bit so the surface gets smoother to cheat around the issue or disable the denoiser which is of course the best option. To get less noise you can also render it a bit more bright, noise tends to be worse in darker corners. If you make the scene brighter you can just darken it again in post. It helps the renderer I think.
I also would suggest not to use both denoise and firefly filter. While they are both different things I noticed that the firefly can also remove tiny gloss reflections while they are part of the render.
If you want you may also share your scene and I can take a look. No guarantees but I like to puzzle a bit with such things and it’s helps me understand KeyShot better.