If you want to make a game that runs locally on someone's computer, you should make it in Adobe AIR. AIR apps can read and write files, and do all sorts of useful things like show updates in the taskbar, etc. Whereas a simple SWF that you download and run locally can't do anything useful that it couldn't already do in the browser - it can't write or delete local files, for a start. (It can read local files, but only if you disable it from accessing the network.) Moreover, the standalone Flash player is not generally disseminated, so unless the user is a Flash developer they're just going to view your SWF in a browser anyway (unless you plan to publish projectors, which I also wouldn't recommend).
With all that said, however, even if you do your game as local flash content, you can still store information by using SharedObjects. They work the same way offline as online. You can't write the data out as a separate file, but you can store it between sessions easily enough.