That doesn't work on a Kindle Keyboard (gen 3). Even
http://time.is fails, though that works on my desktop.
It seems to only connect to websites with no https version.
Also how much webtraffic is that? Though it should be minuscule. A clock that needs the Internet is a bit iffy.
I'd not buy a wall or LCD "radio" clock that doesn't have manual setting as sometimes reception of the transmitter is too poor.