I have removed Deskop Experience from Windows Server 2012 R2 using:
Server Manager -> Manage -> Remove Roles and Features -> Features - User Interfaces and Infrastructure -> deselect Desktop Experience
Or uninstall it from Power Shell (don't forget "Run as Administrator"):
Get-WindowsFeature Desktop-Experience | Uninstall-WindowsFeature
-Restart to the end of the command above and server will restart automatically.
Server did not end up in headless mode, restart was is required.
On the other hand, two options Graphical Management Tools and Infrastructure and Server Graphical Shell next to Desktop Experience item will remove GUI and make server headless.
Adobe Flash Player in Internet Explorer is part of the Windows Experiece feature and Windows updates are available for it.
More details about Adobe Flash Player in Internet Explorer.
Windows Experience contains:
Windows Media Player, Windows SideShow, Disk Cleanup, Sync Center, Sound Recorder, Character Map, Snipping Tool, Support for desktop apps, Windows Store etc.
More details about Windows Experience.