Linux Theme Store Problem - jeeeyul/eclipse-themes GitHub Wiki
SWT Browser dependency is pretty complex to common users. Default installation of Ubuntu doesn't meet the requirements of SWT Browser Support. As a result Theme Store will not work.
Below script will resolves most cases:
$ sudo apt-get install -y libwebkitgtk-1.0-0 # when using gtk2
$ sudo apt-get install -y libwebkitgtk-3.0-0 # when using gtk3
Then restart your eclipse and open Theme Store
again.