The lights and outlets may be on individual breakers but I'd bet they share a neutral.(The white wire) If you pull a seperate ground for each circuit, the flickering should be eliminated.

Note, If they do have a shared neutral, you can still have power on the white even though you have the breaker off. i.e. Find the feed to the room. Turn off the breaker for the outlets. Disconnect the white and see if the lights go out. If they do, you have another breaker using that neutral. You are also working live so be careful not to touch anything. You shouldn't depend on a breaker being turned off to have a dead wire anyhow. Always test the wire for voltage before you touch anything.