Hello,
Since your users do not have Admin rights to install software, you'll want to disable auto-updates on each machine. The update settings are stored in the /Library/Application Support/mms.cfg file. You'll want to make sure the AutoUpdateDisable and SilentAutoUpdateEnable settings are configured as follows:
AutoUpdateDisable=1
SilentAutoUpdateEnable=0
This will disable ALL updates for these machines, as such, you'll want to distribute updates via some other mechanism to ensure your users have the latest secure versions when they're released.
Enterprise deployment information is documented in the Adobe Flash Player Administration Guide for Flash Player | Adobe Developer Connection.
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Maria