Can't Select Home Directory for JDK because IntelliJ can't see it?

You can try installing IntelliJ IDEA from here and see if it works better. .tar.gz distribution can be launched using ./idea.sh. Note that you can also create a launcher script using Tools>Create Command-line Launcher. This should work with any version.

I had the same problem with IntelliJ installed with Flatpak on Fedora 29. I believe (but correct me if I'm wrong) that Linux Mint's Software Manager also uses flatpaks.

It turns out this is one of those "it's a feature not a bug" situations due to the way Flatpak sandboxes applications. As per the documentation at http://docs.flatpak.org/en/latest/sandbox-permissions.html:

Sandbox Permissions One of Flatpak’s main goals is to increase the security of desktop systems by isolating applications from one another. This is achieved using sandboxing and means that, by default, applications that are run with Flatpak have extremely limited access to the host environment. This includes:

No access to any host files except the runtime, the app and ~/.var/app/$APPID. Only the last of these is writable. No access to the network. No access to any device nodes (apart from /dev/null, etc). No access to processes outside the sandbox. Limited syscalls. For instance, apps can’t use nonstandard network socket types or ptrace other processes. Limited access to the session D-Bus instance - an app can only own its own name on the bus. No access to host services like X11, system D-Bus, or PulseAudio. Most applications will need access to some of these resources in order to be useful. This is primarily done during the finishing build stage, which can be configured through the finish-args section of the manifest file (see Manifests).

One way around this is to install JDK versions using flatpak as well, eg.

flatpak install flathub org.freedesktop.Sdk.Extension.openjdk9 org.freedesktop.Sdk.Extension.openjdk10 org.freedesktop.Sdk.Extension.openjdk11

Another way around this is the solution CrazyCoder provided, which is to install IntelliJ using their tar.gz. This eliminates the entire sandbox constraint altogether.

As others said - sandboxing is a feature not a bug.

I think @Kevin Dubois's answer should perhaps be preferred where applicable (you can install via flatpak the thing you want to share), but there is another solution to this problem if you would like to continue using flatpak

How to find /etc and /usr paths in a flatpak:

As mentioned at the end of this section of the documentation, these two directories are mounted under these new paths in flatpakked software:

• /etc at /var/run/host/etc
• /var at /var/run/host/var

How to find other paths in a flatpak:

NB: It is generally a good idea to give software as little extra access as possible. That's why it is preferable to use the optional :ro suffix when granting access to a path to make it accessible in read-only. You will also be partly responsible if some software abuses the access it has to your device.

Examples using the path /var/lib/gems and the flatpak com.jetbrains.IntelliJ-IDEA-Community:

To grant access:

sudo flatpak override --filesystem="/var/lib/gems":ro com.jetbrains.IntelliJ-IDEA-Community

To check current permissions:

flatpak info --show-permissions com.jetbrains.IntelliJ-IDEA-Community

To forbid access:

sudo flatpak override --nofilesystem="/var/lib/gems" com.jetbrains.IntelliJ-IDEA-Community

To reset permissions:

sudo flatpak override --reset com.jetbrains.IntelliJ-IDEA-Community

There's some useful path variables in the filesystem permissions reference and a lot of additional information about filesystem permissions here.