The only thing that's really in your control is which browser you use. You might want to experiment with Edge, Chrome and Firefox. They all use a significantly different Flash Player variant, and have different amounts of overhead.
Flash Player is a language runtime. We processes the code that the content provider writes, and we do the low-level stuff like allocating memory and drawing pixels on the screen. If the content provider writes code that executes slowly, then the browser will eventually step in and mark the page as unresponsive. There's no magic bullet that we can generically apply to all content that would fix this.
We *do* provide a nice profiling tool for content providers called Adobe Scout, which allows them to identify and fix slow code. This is something that the content provider ultimately needs to troubleshoot. In the unlikely event that they identify an actual language-level issue, they'll be able to reach out with a technical analysis; however, it's much more likely that they'll find an easy opportunity for optimization and they'll fix it with a few lines of code.
The only other thing that jumps out me is that maybe they're handling the webcam feed poorly. If they're trying to rescale the webcam feed because your new laptop provides a higher resolution video than they want, then they have to basically process every pixel on every frame. That would be expensive from a CPU perspective. If you can find an old USB webcam (that records at a lower resolution), and that magically makes the problem go away, then that's probably what's happening. I wouldn't run out and buy one until you know it works, but if you can borrow one for a few minutes and try it out, it might give you a decent workaround. Also, if that's the case, it's something the content provider should be able to optimize. (The really high resolution webcams showing up in laptop chassis are a relatively new thing, so it may just be something new that they need to optimize for)