I live in Flagstaff but have never ridden to Phx. The quickest route, by car anyway, is down Interstate 17 but that wouldn't be too pleasant on a bike. I'd consider heading down Lake Mary Road (Forest Highway 3) from Flagstaff, hang a right onto Highway 87 and follow that all the way into Phx. It is for the most part a two-lane road the entire way without the greatest shoulders. The traffic isn't terribly heavy except on weekends, especially holiday weekends. The route is beautiful but does have it's share of hills but Flagstaff is much higher in elevation than Phx. so you'll generally be going downhill with just some relatively short climbs.
You could also go from Flagstaff to Prescott via Highway 89a and then down toward Phx. through Congress Junction etc. That is another beautiful route.
The route jcrouse suggested is the prettiest. It takes you along Mormon Lake and into the ponderosa pine forest all the way down to Payson. Then Payson to Mesa is open desert hills. I don't reccomend doing the Grand Canyon connector route. It's boring desert terrain with full sun exposure the whole way. Winter conditions in Flagstaff are not usually bad the first week of November. Today warmed up to 70 degrees. The Amtrak will drop you off in downtown. It's worth while to check out downtown as it has developed into a cycling friendly city. Since your into photography, I would think that Sedona is also a can't miss. I'm lucky to live here.