We get this call in tech support occasionally, so I thought I would share this info......
The most common cause for lights on one circuit flickering, when a dimmer on another circuit is moved is neutral interaction. This happens when power is back-fed from one lighting circuit to another, causing the lights to flicker. LEDs are more sensitive bulbs and often are effected more by neutral interaction. There are a few ways to possibly reduce or eliminate neutral interaction.
1. Try putting an incandescent bulb on the lighting circuit that is flickering. Often times, this will help stabilize the circuit and reduce interaction. Although, it is not guaranteed.
2. Run a separate neutral back to the circuit breaker for each lighting circuit. This will prevent the back-fed power from traveling up the other neutral.
3. Replace one of the dimmers with a simple on/off switch. Not the ideal solution, but it will prevent that back-feed of power.