Install gnome classic on Ubuntu 16.04
Solution 1:
If you want GNOME Flashback (fallback), run this.
sudo apt-get update && sudo apt-get install gnome-panel gnome-flashback gnome-session-flashback indicator-applet-appmenu
You will then have options for either GNOME Flashback (Metacity) and GNOME Flashback (Compiz) available when you logout and get back to the login screen.
Solution 2:
The latest version of Flashback was released last year, so it hasn't been updated in a long time.
However, according to this Ubuntu Forums thread, it should work fine. Really, the best way to see is to try it out yourself.
If you like the panels and all the fun things from GNOME 2.x, you may want to think about Ubuntu MATE. It's an updated and maintained version of GNOME 2, with an official 16.04 release.