According to the Flatpak site, you have to install the Flatpak base first, which is only officially available for Fedora, Arch, and Ubuntu, with unofficial/testing/backported ports for a couple other distros. There is no source download I could find on the site, which is necessary to build it for unlisted distros like Slackware (though I suspect its strict reliance on systemd would cause issues there anyway).

This all flies in the face of their marketing statement "The days of chasing multiple Linux distributions are over"; you can't claim a one-size-fits-all system if it only fits six out of hundreds of distros.

Edit: To the downvoters, please reply instead, and tell me why you disagree with what I wrote. If I'm wrong I'll own it.