Solution 1:

I am also getting this issue with Intel integrated graphics on my Dell XPS 13 after upgrading to 16.04 LTS.

Let's see if we can fix this together. Can you copy-pasta the output of the following terminal commands:

sudo su
*password for super user*
lshw -c video

Tell me what you get and if it's similar to my trouble maybe my solution attempt will work for you.

UPDATE: I use Intel Integrated graphics for my machine so I think I have a solution. I will update by the end of the day, but it seems to be working fine with dual display at work. I did the following:

sudo su
*password for su*
apt-get install --reinstall xserver-xorg-video-intel
dpkg-reconfigure xserver-xorg
apt autoremove

UPDATE: The above stopped my screen from flickering until I opened google chrome, or chromium. I believe this may be related to gpu optimization in chrome and chromium. I will look into this more and clean up this update when I have narrowed the problem down.

Final UPDATE: I pushed a short bash file to my github page that definitively solves this problem for intel integrated graphics users. You can download it and run it from https://github.com/0xSteve/Ubuntu-16.04-LTS-Bug-Fixes-for-Dell-XPS-13

If my answer helped you please give me an up vote and help me make better posts in the future by commenting.