Best answer (for now):
from: https://lists.launchpad.net/ubuntu-phone/msg03337.html
We'll still just support the old Nexus 7 for now, as we first need to
start the port for the latest device. It should work, but the main
problem is that the device is based on Android 4.3 by default, so it
requires us to make our layer compatible with that as well (at least
the 4.3 based binaries).
Don't have the device, so can't give more details, but don't see why
not (we would at least have the same possibility to distribute
binaries, so we could also produce such a build once the port is
done).
Update, 27-Feb-2014:
I have Ubuntu Touch 14.04 beta (build 209) running on my ASUS Nexus 7 (2013), 16GB, WiFi device. (I also updated my LG Nexus 4, 16GB smartphone, to build 209, using same method.)
I used the new ubuntu-device-flash tool. The code itself is based on the (fairly new) AOSP ('Android Open Source Project') 4.4.2 source code, and is a major improvement over earlier efforts.
Be patient.
The instructions on 'Install' page are partially updated, but do show how to do the install.
Flashing a phone/tablet with Ubuntu
Once I have this repeatable, I will post details (if 'Install' page not updated) ..