How do I seal overlapping sections of flashing around the perimeter of my house?
The Z flashing is there to prevent water from creating water damage as you have noticed. The flashing is usually overlapped and that is sufficient unless in a windy area then a very small bead of calk between the overlapped flashing can be used but is not needed when properly installed. When I used to build homes on the west coast we would lap the flashing with the west most flashing on top so that driving rain would not be pushed under the overlap even if lapped in the opposite the metal to metal contact should be enough with good siding. There were some siding products "LP composite" that even with proper flashing failed (big class action lawsuits). I don't think brazing will do much more than proper lapping.