I just upgraded to Ubuntu 18.04 from 16.04, and see that most of the emojis are working fine, but some of them are still displayed in black and white. The problem is with Google Chrome and the default terminal (haven't tested other apps yet). All emojis work fine in gedit and Firefox.
In particular, I am not able to get the country flags to display correctly.
Also, on e.g. Emojipedia & Facebook all emojis are displayed fine (even in Chrome), but some country flags (like the German one) and for example thinking face do not show up in the browser tab title. Others, like smiling face with 3 hearts are displayed properly (in color) in the browser tab title.
I've tried installing the emoji font as recommended in this answer, but Ubuntu claims it's already at its newest version:
fonts-noto-color-emoji is already the newest version (0~20180810-0ubuntu1).
I know it sounds like a silly problem, but I am designing a chatbot and need to use emojis there - it's pretty tough to do it if I don't see what the end user is going to see. I was completely unable to get it to work on 16.04, therefore upgraded to 18.04. But still no success.
If it helps, I am using Google Chrome 73.0.3683.86 (Official Build) (64-bit).