Ok.
Yes I'm an electrical contractor and yes, I know the difference between series and parallel ( to whoever asked).
Lights in general can be wired in series, however, can light housings nowadays usually come equipped with a termination block that automatically makes them wired in parallel.
I was stating in that diagram that the 12/3 wasn't ran correctly between switch boxes. That's all.
I saw all text informing the reader it was incorrect.
A lot of times flicker on can lights, especially between 2 3ways is due to not having the correct switches. Lurton Maestro is a good series of switches that can be used.