As of 2016-06-13, the only mean to watch Netflix on Linux is through Chrome. If Chrome is not available in your distribution, you cannot watch Netflix. Since Chrome is not available for Linux ARM, you cannot watch Netflix on any ARM devices, including pretty much all devices Ubuntu Touch is actively worked on. Note that one can get a Ubuntu Touch image for x86 systems here.
Chrome comes with the Widevine extension which Netflix use. This extension complies with Encrypted Media Extensions. Google acquired the technology on December 3, 2010 by buying Widevine Technologies inc.
There was a campaign on Indiegogo named World's First True made for Linux/Ubuntu x86/x64 Tablet where an Intel tablet is proposed. Since it was Intel based, Chrome should have worked on it. But alas, the campaign failed to raise the money.