How to clean the emergency drain tube on a Samsung Ecobubble washing machine?
Causes

Mold/algae/bacterial slime is one cause for drains that don't drain.

The second is mineral build up, but since the drain is rarely used and never dries up I'd say it's probably biological slime. 

The third is hair/lint, so definitely a possibility. 

The fourth possibly is that by design the water passes through the filter before it gets to the emergency drain, so a clogged filter would actually prevent water from draining through the emergency drain. 

Solutions

I'd try filling your washer with a 1:10 bleach to water ratio, and running an empty wash cycle but pausing it before it drains, waiting an hour, and then draining with the emergency drain. Using the emergency drain a few more times like this might help clean it out. 

If you're able to able to blow compressed air backwards through the emergency drain and into the unit, that might help declog it. 

If that doesn't work, then it might be clogged with hair/lint. You might be able to put drain cleaner in your washer, but that would probably risk destroying it. You'd probably be better off disassembling it and removing out the clog from the inside, or trying to stick a flexible pipe cleaner up the drain tube if you have one long enough. 

Enough compressed air through that emergency drain tube will probably clear it though, keep it under 20-30psi though. 

Also maybe clean your filter more often and the emergency drain will drain better if the filter isn't as clogged.