How do I diagnose fluorescent light flicker?
Flickering and buzzing where bigger problems with magnetic ballasts and cheaper type T12 Fluorescents. These are becoming obsolete, if you have these types of lamps and ballasts you can retrofit them out to the newer High Power Factor electronic ballasts and type T8 lamps, or LED tubes. 

T8 fluorescent lamps are about $3.00 each and A ballast is about $17.00. LED tubes are about $8.00 a tube but you still have to retrofit the fixture.

Good luck.