Since you are running Microsoft* Windows* 7 on a system having only 1 GB RAM, I believe 1 GB would not be enough for graphical usage like Flash games.
So I would suggest increasing the RAM at least to 2 GB or 4 GB if possible, keep in mind that this is only a suggestion, I cannot guarantee that only by increasing the RAM the system will have very noticeable performance increase, but it might help.
Also you might want to contact the game developer to ask them what hardware configuration is the recommended to run their game.
