Without labeling the relay contacts (normally open, normally closed, common) I can't really critique your diagram, but it seems to have more ground connections than needed.
I would suggest keeping it simple and not using the relay. It really won't buy you much.
Use NCSExpert to code off the bulb check. That eliminates the bulb out warning and the strobing when you first turn the ignition on. (Although I kind of like the strobing, but that's just me.)
Not sure about the flickering. I just put LEDs in my stock halos, coded off the bulb check, and I'm fine.
Are you sure it's not a loose connection that vibrates open/closed from the engine vibration?
It might also be the LCM frantically trying to figure out if the bulbs are good or not.