Look for the most simple possibility. Say for some reason the Kingair rudder trim was offset before the pilot entered the aircraft. Accept that why it was offset is not determined. I haven't flown a King Air but would an offset rudder trim show up while taxiing? In other words is there a nose wheel steering connection like a 737?
A 737-400 crashed during a botched abort in USA and the rudder trim (electrically operated from the cockpit) was found to be full scale one side. The captain was taxiing but the F/O was doing the takeoff and soon discovered the aircraft was pulling to one side during the early part of the takeoff roll so he applied corrective rudder but to no effect. The captain took over and delayed aborting initially. When he finally aborted his procedure was incorrect and the aircraft went off the end into a river.
The point here was with the 737 the fully offset rudder trim causes the rudder pedal to move by about three inches. This because there is limited nosewheel steering availibility with the rudders. The pull to one side taxiing is immediately noticeable. To correct for this, the captain uses his nosewheel steering wheel to keep the aircraft straight while taxiing. In other words similar to crossed controls.
In the case of the 737 accident there was CVR evidence the captain did not mention to the F/O there was something strange happening that required the captain to use excessive nose wheel steering to keep the aircraft tracking straight while taxiing.
Unless the F/O just happened to be keeping his own feet on the rudder pedals while the captain was taxiing (very unlikely) he would not have seen the split rudder pedal position on his side since it would have been only a couple of inches difference.
Once lined up for takeoff and when the captain handed over control to the F/O for take off, the aircraft would have tended initially to pull to one side which the F/O would have corrected for by rudder.
As the aircraft picked up speed during the takeoff roll it gets more difficult to keep straight. When the captain in the 737 realised the F/O was having a problem with directional control and took over control the aircraft was well off the centreline.
So that was what happened to the 737 according to the NTSB accident report. We replicated that in the simulator. As mentioned earlier I have not flown a Kingair so know nothing about its taxiing characteristics with its rudder trim fully offset. But if its rudder pedal steering system is tied into the rudder trim system, then this would have been obvious when taxiing as it was in the 737. That being so it would have been unwise to takeoff.