I've never hiked the trail, but the road to Bear Flat is sedan accessible, as is FR200 on the east end at Gordon Canyon. Though it's an easier drive via the Young Road than from Colcord Road if you don't have a high-clearance vehicle.
More importantly however is that right now, the Bear Flat Trailhead is closed due to black bear danger
. It is scheduled to be open again September 5th. In the meantime, keep an eye on the Tonto NF website.
Maps and links, plus discussion in this thread:viewtopic.php?f=2&t=7045&p=83538&hilit=bear+attack#p83509