How thick to pour slab over existing brick patio
You can go with whatever thickness you like, however, if you want it to last, you need to determine if the brick will continue to settle and crack. If so, thicker is better or your cracks will eventually show up in your slab. 4" would be the best, with expansion joints. You might be able to get away with 3" with more joints, but you'd be pushing it and possibly inviting cracking. A standard sidewalk is 4" thick, and even they crack from settling. 1" is just a skim coat and will definitely crack. You can't make up 4" by using your 2" brick, plus 2" slab. The brick below will continue to move and seperate from the slab, causing more cracking. Your best bet....remove the brick and level, grade, gravel and then pour a new slab, 4" minimum with proper expansion joints. Not cheap however.

What will this slab hold? Heavy weights like a vehicle? If so, you will want 6" minimum.