I can't play or stream online videos with MKV extesions in Firefox though I can play these videos through Chrome. It says "The media could not be loaded, either because the server or network failed or because the format is not supported." while trying to play the video.
I am Using the latest Firefox for Ubuntu 16.04
Unfortunately its simply not supported.
There is bug on Mozilla's Bugzilla - https://bugzilla.mozilla.org/show_bug.cgi?id=1422891 but without much of progress here.
.Mkv and/or other video files can be played through firefox and firefox mobile by either right-click/long-press on video link for play options then choose the video player you know sorts the file example VLC player on Android market.