One meaning of 'fly', as an adjective, is 'cunning' or 'crafty'. Its use in the construction 'fly-tipping' is probably related to this idea...that is, someone creeps up - as it were - to a quiet spot where he won't be spotted and dumps his rubbish in an underhand sort of way.
alternatively, 'on the fly' means while in motion, so a fly-tipper could be someone who dumps his rubbish out of a car window, say (or perhaps gets out and does it but leaves his motor running, literally or metaphorically), and then rushes away before he can be caught.