I followed the instructions to download and unzip the AstroImageJ-version v3.2.0 20160201_linux.tar.gz into my user space on a Ubuntu MATE 16.04. It starts OK but there are no apparent tool bar icons for Astro-Mode or other custom icons.
When I try the install plugin (compile and run) and select the Astronomy_.jar the error message is "filename must end in .java or .class". When I try plugins->shortcut->install plugin the message is "no plugins found".
BTW this is a first test to learn about AstroImageJ for relative photometry intended for exoplanet work by an amateur astronomy club which has a 0.5 m RC scope.
Can you please confirm that you have completed everything listed in the above installation document? If so, and if you are still having trouble, I'll try to get you help from a colleague that has much more linux experience than I do.