Hello: having exact same symptoms, so I decided to try your steps and post my results as well. hope that's OK.
I tried to install and capture the log files in Console as you had directed, see log snippets below:
FlashPlayerInstallManager.log
Marker - Sep 15, 2014, 7:26:03 PM
2014-09-15 19:33:43 -0500 [I] IM: ---------- log start ----------
2014-09-15 19:33:43 -0500 [I] IM: All install checks pass
2014-09-15 19:33:52 -0500 [I] IM: User does not have any processes that need to be closed before the Flash Player can be installed.
2014-09-15 19:33:52 -0500 [I] IM: [install started]
2014-09-15 19:35:58 -0500 [I] IM: ---------- log start ----------
2014-09-15 19:35:58 -0500 [I] IM: All install checks pass
2014-09-15 19:36:05 -0500 [I] IM: User does not have any processes that need to be closed before the Flash Player can be installed.
2014-09-15 19:36:05 -0500 [I] IM: [install started]
2014-09-15 19:53:44 -0500 [I] IM: ---------- log start ----------
2014-09-15 19:53:44 -0500 [I] IM: All install checks pass
2014-09-15 19:53:44 -0500 [W] IM: Unexpected umask value for process: 0
2014-09-15 19:53:44 -0500 [E] IM: User has 1 process that needs to be closed.
2014-09-15 19:53:44 -0500 [E] IM: Install failed with error code: 17.
2014-09-15 19:53:44 -0500 [I] IM: ---------- log end ----------
2014-09-15 19:54:29 -0500 [I] IM: ---------- log start ----------
2014-09-15 19:54:29 -0500 [I] IM: All install checks pass
2014-09-15 19:54:29 -0500 [W] IM: Unexpected umask value for process: 0
2014-09-15 19:54:29 -0500 [I] IM: User does not have any processes that need to be closed.
2014-09-15 19:54:29 -0500 [I] IM: [install started]
Install.log
Marker - Sep 15, 2014, 7:33:21 PM
Sep 15 19:33:54 Jasons-iMac.local installer[7018]: JS: Flash Player Install: Performing volume check for /Volumes/The DeLorean
Sep 15 19:33:54 Jasons-iMac.local installer[7018]: JS: Flash Player Install: Error: Non-OS Volume detected.
Sep 15 19:33:54 Jasons-iMac.local installer[7018]: JS: Flash Player Install: Performing volume check for /Volumes/Tyrone the Media
Sep 15 19:33:54 Jasons-iMac.local installer[7018]: JS: Flash Player Install: Error: Non-OS Volume detected.
I also tried to run in debug mode, here is the host.developer.log file as you had requested.
Let me know if you can find a solution to the problem! I've been on looking for a fix for what seems like months. Please help!