Can Flash Player be installed on an external hard drive?

I have this game I am trying to install on an external hard drive that requires Flash Player and even though it is installed on my computer the game keeps popping up with Flash Player is required for this install. Would you like to install it now? Is there any way to install Flash Player on my external or get the game's installer to recognize it being on the hard drive. I don't want to install the game to my computer. Thanks for any help.