It appears to have been a bad breaker. I swapped the wires between 2 breakers and the flickering moved to the other circuit almost immediately. It was a dual breaker and it looks like one breaker went bad.
The circuit that was flickering probably gets more use than any other circuit in the house. There's a couple of living room receptacles with lamps plugged in, the basement ceiling fluorescents, 2nd floor landing light, basement landing light, kitchen ceiling fixture, etc. These are lights that are used every day for hours at a time.
Anyway, I changed the breaker. Since it was an intermittent problem, we'll wait and see, but I'm pretty sure the problem's been solved.