SOLVED: Adobe staff member Chris Campbell posted this alternative Adobe Flash v14 installer from macromedia.com that solved my problem instantly!
You'll see that the installer looks a little different than the standard v14 installer from Adobe.com (the one I was taken to when prompted by the autoupdater). I don't know if it's an older style of installer or a newer one, but the install happened super fast and without a hitch. Good luck!
Same problem on iMac with OS X 10.9.4.
Using -debug mode of the installer, I see error code 30. This is the same as the problem with Flash Player v13, which if memory serves, was some kind of invalid CPU instruction in the installer, which in turn apparently only occurred on Macs sold between 2009 and 2013. (Obscure Intel chip bug or something?)
The problem was fairly swiftly remedied for v13 but seems to be lagging a bit for the latest v14. How do we notify the right people at Adobe directly - since it seems unlikely they'll be reading this. :-/
Oh ... a work around for the v13 problem was to roll back to v12. (There was a direct download link somewhere that I followed.) However, that version is now blocked from running (presumably) by Safari v7.0.5 on my system.
The link in the previous post is now a 404, by the way and I'm not sure it was trustworthy in any case.