I noticed a small problem on my '69 RS/SS last night. I had to switch on the hazards and noticed that the front parking lights flashed as normal, but nothing in the rear.

My brakelights and turnsignals work fine. Any ideas as to how this could happen? Do I have a faulty switch or flasher?

You can switch the flasher from the turn signals to the hazards and see if that cures the problem. Then your flasher is bad. Otherwise, check your wires running from the switch to the hazard itself.