To create a seemingly random sequence of flickers, we'll create three separate looping sequences and let them fight it out. We'll select prime numbers for their durations (29, 13 and 17 frames), so that it will be a very, very long time before their alignment repeats. And even when it does, the initial condition of the output will be different. Each sequence will also try to ramp the output to different levels and at different rates. So for all intents and purposes, the effect will never repeat itself.
Observing the results, this combination produces a very convincing candle. For a lantern or fireplace, make one or two of the sequences loop more slowly. to simulate larger flames.
Because this effect uses only a single channel, it's easy to duplicate it so there are three sequences controlling every flame in the attraction -- each on a separate dimmer. Simply start the sequences looping at different times during the start up routine, and they will all be completely different from one another.
Another trick is to use a spotlight to reinforce the flicker. This works particularly well for lanterns, where the flickering bulb in the lantern is reinforced by a glowing circle around it. Simply wire both light fixtures to the same dimmer channel.