Flagstaff, Arizona sits in the middle of the San Francisco volcanic field and at the northern end of the Lake Mary fault which poses a potential earthquake hazard for the city. The Lake Mary fault (yellow lines in map below) extends about 25 miles from Mormon Lake in the south into the city of Flagstaff on the north.
Dr. David Brumbaugh, Arizona Earthquake Information Center (AEIC) at Northern Arizona University, estimates that there is 50% chance for a magnitude 6.9 to 7.0 earthquake sometime in the next 30 years. Such an earthquake could do great damage especially to older structures in town. Three such earthquakes have occurred in the region between 1906 and 1912. A swarm of very small quakes occurred along the fault this past June.
Flagstaff lies astride the Northern Arizona Seismic Belt and is considered second only to Yuma, Arizona for potential seismic hazard.
The Arizona Geological Survey has two featured sections near the bottom of its webpage dealing with earth fissures and earthquakes. Take a look at the earthquake hazards page here for some information on past Arizona earthquakes.