I have currently installed from Adobe the following applications:
Adobe Bridge CS6 (64bit)
Adobe Bridge CS6
Adobe Dreamweaver CS6
Adobe Encore CS6
Adobe ExtendScript Toolkit CS6
Adobe Extension Manager CS6
Adobe Fireworks CS6
Adobe Flash Professional CS6
Adobe Illustrator CS6 (64bit)
Adobe InDesign CS6
Adobe Media Encoder CS6
Adobe Photoshop CS6 (64bit)
Adobe Prelude CS6
Adobe Premiere Pro CS6
Adobe SpeedGrade CS6
Adobe Flash Builder is not installed.
Adobe Premiere After Effects is not installed.
I've just downloaded Adobe Flash Player 13, but .flv files and .f4v files are not played by Adobe Flash Player. I've tried to make it default player but i didn't release which file .exe to browse for (by right-clicking and choosing Open with > Choose default program...).
There's a Flash Player Projector (standalone) in the Flash Professional CS6/Players folder, but it's usually outdated.
When browsing to an app to use from the Properties window, go there, but... download this one: Windows Flash Player 13 Projector and replace the Flash Player that's in that folder.
If you're looking to test Flash files you've authored, then you'll need the Projector, but if you're just looking for a good player for FLV and F4V, then you should use VLC Media Player. http://www.videolan.org/
Just to clarify: the standalone player (Projector) can only play .swf files.