The current flow through the dock connector is dependant on the power supply that you connect it to as well as how much the device tries to draw from the supply.
The iPad is the most power hungry (of the Apple mobile devices) and its included power supply gives out around 10W max. which = 2 Amps at 5 volts.
You'll find most USB charged/operated devices draw between 500mA and 1.2A. iPhones are around the 1A usage mark.
The power usage will fluctuate depending on how the device is being used - charging whilst being used or just charging.
You'd have to find out the composition of the cables inside, their length and their cross sectional areas (find out their typical resistance) to find out how much current it could actually take before burning out.