To download and install Eclipse using Flatpak, you will need to install Flatpak (if you haven't already) and then add the repository in one of two ways:

Installing via GNOME Software

If you are on Arch, Debian Stretch (or later), Endless OS, Fedora 25 (or later), Mageia 6 (or later), or OpenSUSE Tumbleweed, you can download the repository file and use GNOME Software to install it. Then you can use GNOME Software to browse all the Eclipse distributions available to install from the repository.

Alternatively, you download one of the following Flatpak reference files and use GNOME Software to directly install your prefered distribution of Eclipse:

Installing via the Command Line

From the command line, run:

$ flatpak remote-add --if-not-exists eclipse

You can then browse and install applications in the normal manner. See the Flatpak command line tutorial for more information on this.