Thanks joecaption for the reply. I have posted four images below that should give you a better idea of the situation. The last image is a picture of the garage that shows how the patio sits on top of it. The garage has steel i-beams that support the weight. It just rained, so, in the close-ups, you can see the water seeping onto the concrete foundation in the kitchen. (I have ripped up some of the floor around the door to expose the foundation.)
Lead flashing is pretty easy to find around here--they sell it at Home Depot and Lowes; I found it cheaper at my local building supply store--it is sold by the pound--a 50 lb roll (approx. 20') of 12" lead runs $120. I chose lead because it is cheaper than copper, easy to bend, and is durable. I was going to go up 7" onto the brick, to tie in above the second brick course and cover any traces of that black tar.
Sure, I understand the design problem of having kitchen and patio at the same level, but I am not in a position to pull down the garage and build a new one to lower the patio. I need to do the best with what I've got--and I've got a bad design. I am on the coast, so we don't get a lot of snow--rain is the big issue. Most of the water runs off the patio but, as you can see from the pictures, the grading is not ideal. There is a low area by the kitchen wall where water pools. I was thinking of installing a channel drain to move the standing water off the patio--being sure the drain slopes enough to move the water out.
My plan with the doorway was to pour a 4" threshold (flashed and tied into the existing masonry) and install a shorter door. The raised threshold would be like a doorway on a boat, you'd have to step over the threshold. Perhaps not elegant, but given the situation, I thought it would be my best hope to keep the water out.
I'd really appreciate any comments and suggestions for other approaches that might be better.