In what location on the filesystem does VVVVVV store your progress through the game when you save in game?
In whatever folder Flash stores its saved data. On Windows, that's
%APPDATA%\Macromedia\Flash Player\#SharedObjects\<random characters>\localhost\path\to\vvvvvv\vvvvvv.exe\.The random characters vary from computer to computer, so you'll have to check for yourself.
(I don't know where Flash stores data on Linux or Mac, but I would expect it's somewhere in your user folder.)
To give a concrete example, if you've placed VVVVVV.exe in
C:\Program Files\VVVVVV\, then your saved data will be in
%APPDATA%\Macromedia\Flash Player\#SharedObjects\<random characters>\localhost\program files\vvvvvv\vvvvvv.exe\.
If you've bought it on Steam, you should go to
%APPDATA%\Macromedia\Flash Player\#SharedObjects\<random characters>\localhost\path\to\steam\steamapps\common\vvvvvv\vvvvvv.exe.
Note that this mean you will lose your saves if you do a generic clean of your Flash saved data.
That depends on your installed version of VVVVV.
Version 1.0 STEAM:
Windows: %APPDATA%\Macromedia\Flash Player#SharedObjects\<random letters>\localhost\<path to steam>\steamapps\common\vvvvvv\vvvvvv.exe
Mac: ~/Library/Preferences/Macromedia/Flash Player/#SharedObjects/<random letters>/localhost/<path to steam data>/steamapps/common/vvvvvv/vvvvvv