The problems are well documented on Microsoft's own support community for the Surface Pro 4, and seem to be related to thermal issues with the convertible. AbbasHaroon posted a thread on the subject way back on January 19th, 2017 and it is now 138 pages long. In fact, there is even a website that is dedicated to covering the issue called FlickerGate.com.
FlickerGate alleges that over 1,800 customers are affected by the flickering display issue. Most of the customers began experiencing problems once their one-year warranties expired, and the root cause seems to stem from hardware components that are overheating.
Some users have resorted to wrapping their Surface Pro 4 in plastic and placing it in the freezer to cool it down enough to have temporary relief from display flickering. However, the problem returns after 10 to 15 minutes once the thermal problems creep back up.
For its part, Microsoft says that it is "aware that some customers have experienced a screen flicker on Surface Pro 4 and are monitoring the situation closely.” The company goes on to state that "customers impacted by this should contact Microsoft support.”
Unfortunately, Microsoft doesn't seem to have a program in place to address any out-of-warranty complaints regarding this widespread flickering issues. Instead, the only recourse that customers have -- for now -- is to go with a $450 out-of-warranty screen replacement.