The term 'Flashover' is a generic term and could mean several things but it is loosely a condition where the insulation falls to such a low level that the voltage will [like water] always seek the path of least resistance. It makes no difference if it is AC or DC, its still electrikery .... and it ALWAYS seeks the path of least resistance.
The insulation is generally compromised by contamination, pollution or mechanical damage and whether its between adjacent phases or earth, when the insulation breaks down, it allows a small current to flow. Over time it increases and damages the insulation allowing the situation to worsen. In cases of 'partial discharge' PD to engineers, it can be across the surface of an insulator [due to contamination] or via voids or internal fissures within the composition of the insulation. The surface PD is a slow gradual process that can take weeks / months to lead to failure and is generally seen as a fern-like or dentifrice-sintilation or dentritic-sintilation. In sub-stations or indoor switch-rooms, you generally know or sense something is wrong when you first enter as you can smell the ozone this process produces, so its wise to vacate PDQ!
The case of DC brush gear flash-over would be caused again by some pollution or moisture usually as a result of deposits of carbon dust building up where it should not.
If there is a weak point or path in / across / through / over / around / under / tunneling through any form of insulation [solid, gaseous -air- or liquid] then the voltage will eventually find it out. Never forget water / moisture is the worst enemy of electrickery except demineralised water that is a pretty good insulator right up to 22kV in modern water & hydrogen cooled alternators.
Its a massive subject and would fill several hard drives !!