Use metal brackets to install a wood fence across an existing concrete 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.

One or two galvanized or stainless-steel washers between the post base and the concrete should do. The latter are thinner and would allow finer angle adjustment. If you don't like the look of the gap underneath, fill it with a fine bead of gray caulk.

That said, there's probably plenty of slop against the post that you can plumb it and add the side screws to keep it plumb even if the base is slightly out of level.

To really make it solid with either approach, use heavy-duty construction adhesive between the base and the post.