A new bright red icon appears on my desktop to conveniently allow me to update the flash installation.
But, how do I know that package is from Adobe?
At the moment when I get a new package I go adobe's site and download from there but it would be more convenient to use the installer already on my machine.
I just wonder if it could ever be a way for someone to slip in a malicious package masquerading as adobe.
See details for the latest and most current update (version 184.108.40.2065) here > 2/5/2015 - Release - Flash Player 16.
If you are enrolled in the "Allow Adobe to install updates (recommended)" background update mechanism, you should have received this update (yesterday) automatically and 'silently' (no prompts).
On the other hand, if you have selected the "Notify me to install updates" option, such notification dialog is normally set to show up within 7 days from the update release date, and please also note that Windows users would need to restart their system to receive the notification.
So, in any case... How can we help you if we don´t see whatever you're seeing? Screenshots may help, but even so... suggest you download it directly using the links provided in the above mentioned-linked announcement and install it yourself. I personally trust no FP 'prompts' lately