I found this (from 2011):
In looking at primary sources on early film, I’m finding the term `kinema’ coming up just as frequently as the usual `cinema’. `Cinematograph’ seems to have been the standard term in the very early days, then `Kinema’ pops up in around 1910-11, is then used interchangeably with `cinema’ - or, if anything, becomes more common - before dying out in the late 1940s. From then onwards (and quite possibly, the whole time), there seems a tendency to use it slightly pretentiously. For example, arthouse cinemas tended to describe themselves as `kinemas’, and continued doing so even when the spelling had fallen out of use.
(Don’t bother reading the subsequent discussion, which is chock-full of ludicrous misunderstanding of the history of pronunciation and usage.)