Depend upon how good the game is. and secondly you willing to spend money. Even if not I know how to promote it not only promote also earn from it. PM me if interested.
I'd like to see a link to your flash game! Off the top of my head I'd say the easiest way to promote a flash game is to submit it to one of the big games sites that accept user submissions: newgrounds? kongregate? mofunzone? I'm sure there is like millions! If you want to keep the game on your website I would use Google Adwords & Facebook Ads. Look for vouchers (google it). Hope that helps.
I know this topic is pretty old but I just wanted to let you know that we've created a list of over 600 good arcade websites to submit flash games. http://letsplaygirls.com/submit-games/