Ubuntu 16.04 Skylake 6th Generation Screen Flickering

@brianjcohen led me in the right direction. The Bug report on chromium had some good discussions on some background on the issue, but apparently it's somewhat of an x.org issue with Intel driver options. You can reference it here if you'd like:

https://bugs.chromium.org/p/chromium/issues/detail?id=606152#c63

To fix it, create or edit the file at /usr/share/X11/xorg.conf.d/20-intel.conf as root with the following:

Section "Device"
    Identifier "Intel Graphics"
    Driver "intel"
    Option "AccelMethod" "sna"
    Option "TearFree" "true"
    Option "DRI" "3"
EndSection

• From the discussion, the AccelMethod should by default be sna, but apparently not explicitly setting it as such could cause X to crash. sna is definitely faster than downgrading it to uxa.
• TearFree helps prevent tears in video rendering
• DRI is a method on how the driver renders things, I think this was the key option. You can find out a whole bunch on what it is here: https://en.wikipedia.org/wiki/Direct_Rendering_Infrastructure#DRI3
• You can also read the man page at man 4 intel

UPDATE: Yesterday, I freshly installed Ubuntu GNOME 16.04. It came with an up to date kernel version: 4.4.0-18. It seems to have solved the Screen Flickering issue for me (at least until now). Aditionally, the physical buttons of the touchpad work as intended (i.e. scrolling and drag & drop are working). There seems to be some Screen Tearing in web browsers (firefox and chromium). But it really is not comparable to the Screen Flickering issue before. In firefox, I managed to get rid off the Screen Tearing by disabling "smooth scrolling" option. Unfortunately, the same procedure doesn't seem to help in chromium.

I had this issue on my new Lenovo X1 Carbon running stock 16.04 (4.4.0-33 kernel, Skylake GT2 graphics). I tried two of the answers above (basicdays and Mike O'Connell's) but neither worked. The former caused the graphics to be unusably slow; the latter failed to initialise the graphics at all.

In the end I solved the problem by the other method mentioned here, that is: I removed the problematic Intel-specific graphics driver. All seems good so far - no flickering in Chrome and some glitchy behaviour in other apps seems to have gone away too.

In short, run this and then reboot and all should be good:

sudo apt-get purge xserver-xorg-video-intel