Voltage Regulator Question
As mentioned, you can buy an electronic regulator that works with your existing round-back alternator. Check rockauto, they list an $11 one that is in a chrome flat pack, but with connectors that match your old one, so a 5 min swap. Unlike 67Dart273, I have seen many new Vreg's in the old black box that are the old mechanical relay type (resistors underneath). At least they look like that in the photos.
Re flickering lights, it probably won't help much. If the terminals weren't corroded or melted, your lights should run fine off the battery alone. Inspect your bulkhead connector and headlight switch connector and clean the terminals. That is equivalent to shaking a flashlight to make it work better (ever do that?), for the many readers who are electronically challenged.
One approach is to add under-hood relays for the headlights. Then the switch simply actuates a relay, which feeds direct battery voltage to the lights. I installed a complete relay/fuse box in my cars for all such switching, as have others.