You know, I think maybe some re-arranging would help. There's something that rings wrong with "shouted at Joe"-- maybe move "Joe" to the next line? That gets rid of the "he" problem (could refer to Kincaid).
Also "said so" rings wrong. Sorry, I can't justify that feeling, but let's see how it looks with the changes:
“Go away!” Kincaid shouted. There was no need to turn in the saddle and look back. Joe was still there. The sounds of creaking leather and the clip of hooves proved that.
"There was no need" is a bit more concise. I wonder if "Go away" sounds angry and macho enough? It sounds more petulant to me, but then, I don't know the situation and character. But here's just an example to show how the dialogue could indicate another sort of person:
"Get the hell away!" Kincaid shouted.
What sounds like Kincaid? I think-- stereotyping here-- for a male character you might go for a bit harder-edged words?
I also wonder if you can sneak in just a bit more setting detail? We get the "Western" feel of the horse travel, but think about something like, "Kincaid stared straight ahead at the (setting detail). There was no need to turn in his saddle and...." That way you get the action of the character moving through the setting-- and of course interacting with the other character. :)