I can't see to find code snippets for making a 120VAC light "flicker"...There is easy code to make a LED flicker, but for a AC power load, you need to use the timer function pluin.
I came across a Halloween flicker routine, but it uses a very long set of state tables to drive the random numbers for a 0-255 light level.
Does such a function exist?
Once you had a circuit to drive the light at 120VAC like many of the dimmer circuits that are out there, you could just use the random function to set the level every half second or so to a new random level. It would probably appear to flicker much like fire light with the right interval settings. You could even randomly choose the next interval to add even more flicker effect. Driving the AC load on or off has nothing specific to do with needing a timer function. Getting 256 levels might need some timing.
There are plenty of Arduino AC lamp dimmer projects. As you might have guessed, googling "Arduino ac lamp dimmer" will turn them up.
Most of those should work. Just use a random number to set a new dim value at frequent intervals.
That said, I have a hard time coming up with an AC light that would like that.
Incandescent light bulb will not.
Fluorescent lights will not.
LED drivers might not.
I think there are filament leds that directly run on mains. That may be the best guess,