As is the case in a lot of B westerns the title has nothing to do with the story. The only connection that Arizona has with The Arizona Kid is that Roy Rogers and Gabby Hayes are bringing a string of horses from Arizona as the story opens. Otherwise the action takes place in Civil War era Missouri.
Roy wants to join the Confederate cause, but friend Dave Allen wants to join the irregular guerrillas that Stuart Hamblen is putting together. Roy has scruples about what Hamblen is all about, he's a Quantrill type raider in all, but name.
Later on Hamblen has his connections with the Confederacy severed by the Confederacy due in no small part to Rogers's instigation. After that capturing Hamblen and destroying his band becomes a personal mission for Roy.
I think it completely ironic that the Confederacy had such scruples about the fictional character that Hamblen plays. They sure didn't in real life have any about Colonel Quantrill, they couldn't afford any.
I will say that the final showdown between Roy and Hamblen's character is nicely staged.
Still this is not one of the best of the Roy Rogers westerns.