[Boom]Fire flicker synchronized across consecutive sectors?

In Boom, is there any way to make the "random" fire flicker effect synchronized across sectors that are touching? So, for instance, I could have a flickering effect on a light in an area that has multiple ceiling heights, without it looking really stupid?

Not really. You can use voodoo dolls on conveyor loops triggering light-change linedefs to create a repeating pseudorandom pattern, but there's no simple way to synchronize random flickering, no.

Do you know of any maps that use that trick that I could look at to get a feel for conveyor speeds/linedef spacing?

Not sure, but the method he's suggesting is involving tripping a bunch of -WR change light to brightest or darkest adjacent- linedef types to simulate the sectortype 17 light flicker effect. In practice you'd probably be spending three or four hours or more just getting it in a state that doesn't look stupid. If it were me I'd probably think of an alternate solution with the lighting or surrounding architecture.