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.
Sodabread
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