Can I install 6' 6x6 fence posts onto a cement driveway?
A fence post has very little vertical force...mainly just the weight of the post and panels it holds. Your driveway slab would work fine as a footing for that. HOWEVER, the primary force on a fence is typically lateral--especially a 6' fence. The reason posts are put into the ground is to counter lateral forces on the fence (typically the wind).

I imagine there are types of brackets that could be used on the concrete to accomodate the lateral forces, but the type you have in your post is not that type...that's typically used to attach structural posts to concrete (it handles the vertical force, but not lateral). 

The type of brackets you'd need would be something akin to a shelf bracket where there's a diagonal brace between the two plates. 

So, one option is to cut holes in your slab and dig proper holes there. Alternatively, you could find plates designed for this (or have someone weld some up for you). 

A third option would be to not build a straight fence, but rather stagger the posts in a zig-zag pattern.