How do I stop Flash Player box about 'accelerating hardware' popping up during games?

When I play various brain-training games on the Lumosity website, a white box pops up from Flash Player with a check-box about 'accelerating hardware'. The box is already checked and cannot be unchecked. The pop-up won't go away without repeated clicking on 'Close' by which time the game is spoiled. A similar thing happens on a Just Words, a Scrabble type game on Games.Co.Uk. How can I stop this interference?

I have checked that I have the latest version of FP installed correctly on my Mac and that these websites are permitted access.

Thanks for any suggestions.