Minimum mobile hardware for playing 1080p with Flash on Win7+

What's the minimum hardware (Intel/AMD) in a laptop needed for playing 1080p video with the Adobe Flash Player without dropping frames or the computer freezing on Windows 7 (or newer)?

Any new laptop should be able to play such content. But any laptop from the past few years should also be capable.

Update the Flash plugin to the latest version and also update your graphics driver. That may solve your problems.

If you right-click on a Flash video you can also find an option to enable/disable hardware acceleration.

I want to buy on eBay the cheapest and oldest USED notebook computer that's able to play dsmoothly 1080p video with Flash, at least in Windows 7

Give me a link to an eBay item that you are considering to buy, and I can say if I think the hardware is capable.