AMD FreeSync For Tear-Free Linux Gaming - Current State In 2017
Turning On FreeSync Linux Support
Checking for and enabling FreeSync Linux support isn't unfortunately as intuitive or friendly as under Windows.
To check if your GPU and display are capable of supporting FreeSync when running on a supported Linux driver stack, you need to run xrandr --prop from the command-line to look at the RandR properties. For each display output there should be a "freesync_capable" property where 0 indicates it's not supported or 1 means the display output / monitor should be capable of handling FreeSync.
While FreeSync on Windows supports HDMI outputs too, FreeSync currently on Linux will just work with DisplayPort connections.
Besides the "freesync_capable" property, there is also a "freesync" property. That property is used for toggling the FreeSync Linux support on/off. If your display output is capable, turning on the FreeSync support is along the lines of running "xrandr --output DisplayPort-2 --set "freesync" 1", depending upon your output configuration.
It's certainly not as nice as Windows with the Radeon Software Settings panel or even now being able to toggle FreeSync via the Radeon Overlay when in-game. Hopefully when the user-space side of the patches land next year for RadeonSI and friends, hopefully it will be able to seamlessly turn on/off FreeSync via DriConf whitelisting games / detecting when a full-screen game is launched, etc.
FreeSync Linux Compatibility Notes
AMD maintains a support page outlining some compatibility notes for FreeSync on Linux currently with AMDGPU-PRO. Namely, FreeSync only works with DisplayPort on Linux right now, only full-screen games / those covering the entire X screen are supported, multi-monitor FreeSync is not supported, and V-Sync must also be forced on for OpenGL Linux games to work. The page does outline how V-Sync can be forced on universally with AMDGPU-PRO via editing /etc/amd/amdrc.
As far as what Linux games/applications are officially supported, the list is a bit of a mess. They mention titles like Team Fortress 2, Dota 2, Counter-Strike: Source (but no mention of CS:GO), Rocket League, and even glxgears. But they also mention the Phoronix Test Suite as supported with FreeSync... That was a bit of a surprise to me as there is nothing PTS itself needs to do for FreeSync. But if it means any test profile will work with FreeSync, then pretty much all major Linux games should be working fine.