I agree your first day would be a real challenge. By the time you get your car and get out of the airport, it will likely be 4:30, meaning you'll be getting on the road in the middle of rush hour, plus you'll have additional traffic at the hoover dam, so it will almost certainly be dark well before you even get to route 66.

I'll also mention that if you do go this way, it would make a little more sense to stay in Williams, rather than driving all the way out to Flagstaff, saving you some driving.

One thing you might consider is reversing your direction, so you'd have a shorter drive to Springdale that first night. Then work backwards, staying in Cameron and then perhaps Williams. That would give you more time to enjoy Route 66 and the Hoover Dam as you make your way back to Vegas.