Fluorescent tubes work by heating cathodes so that they emit electrons and allow an electric current to flow from end to end in the tube. The tube is filled with a gas (usually argon) at low pressure, which becomes ionised and conductive, and mercury vapour resulting from energy imparted to the small amount of mercury in the tube. The electrons and argon ions collide with the mercury atoms which excites them into a higher energy state. The atoms subsequently return to a lower energy state releasing a photon from each atom in the UV region. The photons are absorbed by fluorescent coatings on the inside of the tube and, by a similar method, re-emit light at visible wavelengths.
Problems that have to be overcome is starting and maintaining the process. The cathodes have to be heated sufficiently to get the emission of electrons and then a high voltage applied between the ends of the tube to ensure that the gas ionises to allow a current flow. The voltage that has to be applied to start the process is higher than the 110V or 240V available, so has to be generated though, once the process has started, can be reduced to a lower value. The process is controlled by having a ballast inductor to limit the current - it provides a series impedance to the AC supply.
There are a number of methods to start the tube. A common one employs a small neon lamp which is in series with, and between, the cathode heaters. When voltage is applied the neon lamp strikes and heats its neon gas. The lamp is contructed with bi-metallic strips for its electrodes so that this heat causes the two electrodes in the lamp to eventually touch. When this happens it provides an increased current to the Fluorescent tube cathode heaters and they get extra hot and emit electrons. The neon eventually cools and its electrodes separate; this causes the inductor to generate a high voltage that "strikes" the tube. From then on the tube is conducting and of a low enough impedance that the starter neon (in parallel with the tube) will not light again and the tubes cathodes can maintain sufficient emissions without the extra heat.
Now to answer your question. When a tube gets old a common failure mechanism is that the cathodes become inefficient at emitting electrons. The result is that the tube strikes but then cannot maintain that state. As soon as it goes out, the neon starter tries to re-initiate the start sequence and this can repeat indefinately. The timing of when the neon breaks relative to the voltage across the tube at that time (remembering the voltage is AC) produces inconsistent and seemingly random results and the observed flashing.
I'm sorry this is so complex, but I can't think of an easier way to explain it.