Depending upon your operating system, you may have to dig some place else, but from a Windows 7 user...
Firefox users: Go into your user's directory (hidden folders must be visible)
AppData\Roaming\Macromedia\Flash Player\#SharedObjects\P6T32G2X\localhost
Chrome users: Same thing as above, again hidden folders must be visible
AppData\Local\Google\Chrome\User Data\Default\Pepper Data\Shockwave Flash\WritableRoot\#SharedObjects\TRG4CGWL\localhost
IE: I haven't the slightest clue, it's an abandoned browser anyways. Win 10 doesn't even have it and uses a different browser. You should too.
Note that those saves will be automatically named "CoC_1", "CoC_2", and so forth, both for the regular game and the Revamp since both share the same save slots. That's where they will appear when using the normal "Save" and "Load" buttons. "Save to File" (and, subsequently the "Load from File" button) will allow you to dictate the save file location upon saving while loading from anywhere freely and is, like MESeele pointed out, the preferred method of backing up your saves. You can also choose the file name as well. Think of "Save" as a quicksave system, but without all the bells and whistles of a full blown save system.
Edit: Those are also the location of your TiTS saves, too.