Kernel 4.4 has been released and should fix most of the issues now. (I have it installed and not experienced any issues so far.
If your XPS 13 (like mine) is equipped with a NVMe SSD you'll have to compile a custom kernel where you enable the nvme module. Otherwise the kernel won't be able to find the SSD.
To do so, do the following:
First get the necessary packages
$ sudo apt-get install git fakeroot build-essential ncurses-dev xz-utils
$ sudo apt-get install kernel-package
$ sudo apt-get install libssl-dev
Get kernel 4.4.
$ wget https://cdn.kernel.org/pub/linux/kernel/v4.x/linux-4.4.tar.xz
$ tar xvf linux-4.4.tar.xz
$ cd linux-4.4/
Copy your current config file
$ cp /boot/config-$(uname -r) .config
Now edit the .config file with your favorite editor to enable the NVMe module.
Search for CONFIG_BLK_DEV_NVME and set it to y (from m)
Now it's time to compile your custom kernel. (the last command can easily take up to 1.5 hours)
fakeroot make-kpkg --initrd --revision=1.0.NAS kernel_image kernel_headers
And install! (ignore the warnings coming from the first one)
$ cd ..
$ sudo dpkg -i linux-headers-4.4.0_1.0.NAS_amd64.deb
$ sudo dpkg -i linux-image-4.4.0_1.0.NAS_amd64.deb
Now just reboot and it should start in kernel 4.4.
Additionally after a few reboots I ran into problem where my screen would remain black. Seems like thereś an issue with skylake and graphical drivers.
For me it was fixed by making a change to the grub file.
sudo nano /etc/default/grub
Then change the line saying GRUB_CMDLINE_LINUX_DEFAULT to
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash i915.preliminary_hw_support=1"
Save and apply the changes using:
Source for making custom kernel: http://www.cyberciti.biz/faq/debian-ubuntu-building-installing-a-custom-linux-kernel/
EDIT: Turns out after a few reboots my black screen is after boot is back.. so this is more of a work in progress.