I met with people from City of Tucson, Tucson Fire Department, and Tucson Parks & Recreation recently, and I believe that TFD and CoT are now working on affecting the Tucson Fire Code with some changes that will include fire art or fire performance to some degree.
At the moment, a performer generally contacts an Inspector at TFD to let him know of plans to perform at a venue, or to ask if it would be acceptable to perform at a venue based on its characteristics. Unforunately, I don't know many people that actually do this, or that are aware that they should. Otherwise, practicing on private property does not require any special permission. I was also informed at one time that street performance is also permitted, but I was not pointed to any information that verifies this.
All-in-all, it seems that if you let your neighbors know what you are doing, and meet with the Inspector so that he can get to know you as a safe performer, you will be not be hassled.