The Flamoji extension was added, and with that comes Custom Emojis! More emojis will be added over time.

You can add custom emojis by scrolling all the way to the bottom of the Flamoji emoji picker, which is in the toolbar all the way on the right.

If you want your own custom emoji, start a private discussion with @[WUT] Adam. You'll need to have the specified amount of coins for an emoji:
Static (PNG/JPG) Emoji 50 coins
GIF Emoji 300 coins