In my 1:1 conversations, custom emoji don't work most of the time. I have to refresh Flowdock about 20 times per day so I can see those custom emoji in 1:1 conversations. Sometimes, even after I have refresh for one 1:1, I'll go to a different 1:1 and it doesn't have the emoji showing so I have to refresh again.
It works fine with built in emoji. This affects all but about 10 custom emoji (and we have 100 or so).