How fast does gangrene spread in a diabetic person?

Variable. There are two types of gangrene. Wet gangrene is dead tissue with an infection and is an emergency because can lead to death. Dry gangrene is dead tissue from no blood flow without infection. This typically spreads slowly - months. Your physician will try and stop the spread of gangrene by getting increased blood flow to the area of necrosis to stop the spread.
Hours to days. It's hard to answer this, as there are many factors that contribute to the spread of gangrene. If it is infected gangrene, the spread may take a few hours until it becomes incurable, whereas, so called "dry" gangrene may persist for days expending slowly. Nowadays, gangrene is promptly treated with surgical debridement and revascularization procedures.