No matter how much I think it, it simply does not make any sense to me. Why an earth, isn't there a button to manually update Adobe Flash Player? What good will it do to download it every single time you want it updated? All the parts are already there in your computer, but there is no reasonable way of telling it to: Go! Update! Now!
It is highly likely, that your browser is 32-bit. You need to be some sort of hacker (like me) not to have a 32-bit browser. So, the assumption is this applies to you.
All the good parts are in C:\Windows\SysWOW64\Macromed\Flash\
On a 32-bit Windows
If your PC is old, then you'll have this. (Or, alternate case: you are a hacker and running 64-bit browser.)
All the good stuff is in C:\Windows\System32\Macromed\Flash\
Triggering the update
NOTE: The version number of the application will change on each update. What I demonstrate here was valid at the time of writing this, but I assure you, the exact name of the application will be something else next month.
The location of the files is ...
For all other browsers than Internet Explorer:
FlashUtil32_12_0_0_43_Plugin.exe -update plugin
For Internet Explorer:
FlashUtil32_12_0_0_44_ActiveX.exe -update activex
Running that command as a regular user will trigger the same process that would be triggered during a Windows login. Since I login rarely, the update almost never triggers for me. I simply put the computer to sleep and wake it up and unlock the screen, which again does not trigger the version check.
This isn't the only stupid thing Adobe does. They don't take your security seriously. Shame on them!