The answers, as always, is: it depends. Databases are often times best with online/browser based games, but Flash, I believe, can write save files to the computer on which it's being played. I don't work with Flash, so I'm not 100%.
In single-player, offline games a save file would probably be the best, as you don't really want to install a database instance for your game. I can't say I'd be ok with someone installing SQL on my machine just to save a game. Although, you can do a persistent/occasional network connection (which puts it in the online game category) in order to write the data to a database on your end.
Figure out what you want your game to be and how the player should be able to play it and you'll most likely have your answer.