How do you repair weep hole flashing in a brick veneer?
As far as I know there is no "easy" method that works. You have to strip the bricks down to that level and replace the flashing. Of course, this makes it an excellent time to consider how much you are or are not in love with brick veneer, since that's removing most of it. If you use a more durable flashing (lead is nice) you might get more than 60 years out of it; of course, if you can get 60 years out of anything it's probably more than you personally need.

You might find considerable cost-benefit in a rigid-foam / stucco replacement for the brick veneer - your walls are likley poorly insulated circa 1950s, and that would add a great deal of insulation to them.