Assuming you have a recent flash player version for intel Mac (I think after version 10.2 something), then you have a System Preferences pane for Flash Player. Click on the Advanced tab, then the top item is Delete browser data and settings.
That would do it...
Older Flash Player versions, go into your own user folder, then Library, then Preferences. You can delete the contents of the Macromedia folder. That should do what you need, too.
And, your Flash Player will be somewhat less responsive until the cache files rebuild again. It's sort of counter-productive to delete those cache files, if you already know you have a very slow connection....
As with other cache operations, the cache files are (in theory, at least) designed to help speed up response, particularly on slow internet connection.