Adobe Flash Player will always be the best way. If it only shows a grey screen, there might be other things it relies on. Can you show the entire source of the tag you got it from? So the <embed> tag.
Make sure you allow flash to save data to your hard drive.
Right click the flash game and select Setting (or Global settings). Under the "Storage" tab, make sure "Allow sites to save information on this computer" is checked.
Best Answer
Right click and "Save As" this direct link to download the game: The link