I am not sure I understand the issue.
For me, the error only shows up in the Stoke log when there are no particles simulated (because there is no TextureCoord channel if there are 0 particles, as there is no place to store the data ). As soon as I simulated some particles, the message disappeared when moving the time slider. You had correctly checked the TextureCoord to be acquired from the Plane, and both the Plane and the Stoke had the same Material #56 assigned, looking for the mapping channel. Rendering in Krakatoa showed the correct colors from the image, same as the Plane.
If I misunderstood the question, please clarify.
Also a bit unrelated, but in case you decide to use that disabled Magma modifier on the stack, please note that the Position operator should NOT be passed through a ToWorld operator when running on a Stoke. The Stoke Particle Simulator’s particles are already in World Space, and trying to apply ToWorld to them would apply double transforms, producing wrong results if the Stoke icon is not at the world origin… JFYI.