Your Alternator has a failing Field coil or Diode
The battery is only used to start the engine, its voltage is 12.3v to 12.8v
After engine starts the alternator takes over ALL voltage requirements, its minimum voltage is 13.5volts, so higher than battery voltage, which is why battery is not used at all when engine is running.
So your flickering lights and voltage gauge, with engine running, means the alternator voltage is fluctuating
An alternator uses 3 Field coils in its outside case to generate AC Voltage, each field's AC voltage is passed thru 2 Diodes to make it DC and usable for the Vehicles electric system
So I would guess one of the fields or a diode is failing causing voltage to jump around, at any RPM
You can test this by unhooking the alternator, unplug its 3 wire connector, that will turn it off
Start engine and see if head lights still flicker
If not then replace alternator, or rebuild it
If they still flicker then you have a loose connection in electrical system
You can only run the engine without the alternator for an hour or so, then battery will be drained and won't be able to restart engine
A more common sign of a completely failed field coil is dimming head lights at idle, no they are NOT suppose to do that, lol
Alternator can only make 2/3's of its rated power with a bad field coil so voltage drops too low at lower RPMs