Even if this is an old question by now, it could help others.
Anyways, I'm using Blender 2.80 right now and had this same exact issue, I tried the currently existing answers in this thread, however, none of them worked. Then, when watching this slightly outdated smoke tutorial, I saw that he had selected the smoke domain and then proceeded to edit its node setup. I figured I would do the same even though it seems the node setup for smoke has changed from 2.79 to 2.80.
There were two nodes here, one Material Output node and one Principled Volume node.

I noticed that the Principled Volume node had a color setting, which was set to be a light grey color. Mind you I had set the smoke color to be red in the flow object of the simulation.
This color setting seemed promising so I clicked it, changed the color from the light grey into a redder color. I then checked the viewport. It had changed, the color of the smoke had actually changed. I had figured it out. I was ecstatic, and suddenly I thought of this thread and thought I would share my findings to help others who might run into this issue.
I do hope this help anyone who might be struggling with the same issue.