I bought a gaming computer 2 days ago with an AMD graphics card and had noticed some extreme graphical issues, so I returned it thinking the GPU was faulty. I picked up a new setup yesterday, RX 580, and am having the same issues as before. I have two monitors, both 1080p (and I think 60hz) one is plugged in via HDMI, the other is DP. The graphics card only supports 1 HDMI port, the other 3 are DP ports. I can 100% replicate the problem when you plug in two monitors and then launch a game. Both screens start to flicker a lot. When you exit the game, the flickering continues. If you exit the game, or launch the game with just 1 monitor(either monitor, and either HDMI or DP cable) the flickering does not occur at all. I have tried updating drivers, reinstalling display driver, turning off enhanced sync, nothing seems to work. The only time the flickering does not occur is when one monitor is plugged in.
Current version of the driver I think is 26.20.13031.5006.. based on the "Radeon RX 580 Series Properties" menu.
This is a photo of what the screen starts to look like(on both monitors) whenever I start to play most games.