This page describes how to render vertex colors associated with mesh data.
Start with default cube, enter Vertex Paint mode and paint one of the edges with red color.
To include vertex colors in material, create and connect Attribute node to Color socket. Only single vertex color set per mesh is supported currently.
Alternatively, using the Armory PBR node connect Attribute to Base Color socket.
Hit Play in Viewport to verify results.
If you are having trouble displaying vertex colors in more complex scenes, invalidating mesh cache may help in case Armory failed to register changes. Hit Properties - Object data - Armory Props - Invalidate Cache.