I'm not an electrical engineer so I dont know the exact causes but I've read where flash experts lament that its very hard to gel a flash to match fluorescent lights for this very reason.
Here is what wikipedia says about the flicker.
Fluorescent lamps using a magnetic mains frequency ballast do not give out a steady light; instead, they flicker at twice the supply frequency. This results in fluctuations not only with light output but color temperature as well [18] which may pose problems for photography and people who are sensitive to the flicker. Even among persons not sensitive to light flicker, a stroboscopic effect can be noticed, where something spinning at just the right speed may appear stationary if illuminated solely by a single fluorescent lamp. This effect is eliminated by paired lamps operating on a lead-lag ballast. Unlike a true strobe lamp, the light level drops in appreciable time and so substantial "blurring" of the moving part would be evident.
In some circumstances, fluorescent lamps operated at mains frequency can also produce flicker at the mains frequency (50 or 60 Hz) itself, which is noticeable by more people. This can happen in the last few hours of tube life when the cathode emission coating at one end is almost run out, and that cathode starts having difficulty emitting enough electrons into the gas fill, resulting in slight rectification and hence uneven light output in positive and negative going mains cycles. Mains frequency flicker can also sometimes be emitted from the very ends of the tubes, if each tube electrode produces slightly different light output pattern on each half-cycle. Flicker at mains frequency is more noticeable in the peripheral vision than it is in the center of gaze.
New fluorescent lamps may show a twisting spiral pattern of light in a part of the lamp. This effect is due to loose cathode material and usually disappears after a few hours of operation.[19]
Electromagnetic ballasts may also cause problems for video recording as there can be a 'beat effect' between the periodic reading of a camera's sensor and the fluctuations in intensity of the fluorescent lamp. When other devices that also flicker, such as CRT-based computer monitors, are operated under fluorescent lighting, the flicker may become much more noticeable.[citation needed]
Full-size and compact fluorescent lamps using high-frequency electronic ballasts do not usually produce visible light flicker, since the phosphor persistence is longer than a half cycle of the higher operation frequency. Operating frequencies of electronic ballasts are selected to avoid interference with infrared remote controls. However, poor quality (or failing) electronic ballasts operating from AC mains may have insufficient Reservoir Capacitance and/or have poor Constant current regulator, thereby producing considerable 100/120 Hz modulation as well as the high-frequency switching modulation.
The non-visible 100 Hz - 120 Hz flicker from fluorescent tubes powered by electromagnetic ballasts are associated with headaches and eyestrain. Individuals with high flicker fusion threshold are particularly affected by electromagnetic ballasts: their EEG alpha waves are markedly attenuated and they perform office tasks with greater speed and decreased accuracy.[20] Ordinary people have better reading performance using high frequency (20 kHz – 60 kHz) electronic ballasts than electromagnetic ballasts.[21]
