As Amazon Prime has adopted DRM protection to encrypt the streaming media, DRM will lock the video and you can only record a black screen instead. To process Amazon Prime videos recording without black screen, simply by toggling off the hardware acceleration feature in browser and it will work again.
Take Chrome as an example, you only need to turn to the browser settings and open System to turn off the Hardware Acceleration feature, the black screen will be removed and you can record Amazon Prime videos without black screen occurred.