Your lights and or dimmer are reacting to the common neutral. LED lights are very sensitive to the dimmer. Many are electronic and common neutral can cause issues.

No pic showing so just basic overview. Can test with reg incandescent light to see if still get flicker. If no, then your fan may need its own independent power....no shared neutral.

You said you have red/black wire setup...do they have their own circuit? (breaker). Guessing no and that can be a source of issue as well.