If you experience constant screen flickering and your external monitor turning off every other 3-5 seconds on a Intel i915, here is how I fixed the issue.

Update kernel

First get and install the current kernel from the Ubuntu mainline PPA, which has a couple of fixes for the Intel i915. At the time this was v4.4.14.

wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.4.14-xenial/linux-headers-4.4.14-040414_4.4.14-040414.201606241434_all.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.4.14-xenial/linux-headers-4.4.14-040414-generic_4.4.14-040414.201606241434_amd64.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.4.14-xenial/linux-image-4.4.14-040414-generic_4.4.14-040414.201606241434_amd64.deb

sudo dpkg -i\
    linux-headers-4.4.14-040414_4.4.14-040414.201606241434_all.deb\
    linux-headers-4.4.14-040414-generic_4.4.14-040414.201606241434_amd64.deb\
    linux-image-4.4.14-040414-generic_4.4.14-040414.201606241434_amd64.deb

Set i915 kernel module options

sudo vim.tiny /etc/modprobe.d/i915.conf

options i915 enable_rc6=7 enable_psr=2 enable_fbc=1 lvds_downclock=1 semaphores=1

After rebooting my system the external monitor worked just fine and still does.