First, I would say that you have 2 issues.
The AC throwing a circuit breaker is an overload situation. The AC is drawing more amps then the breaker is designed for. It could be a stalled fan, shorted wire, bad start capacitor or a bad compressor.
A GFCI receptcal is a not for overload protection but a shock prevention device. It looks for an imbalance of the current flow. That imbalance may be voltage traveling thru your body, rather then returning to the outlet. That could be related to the transfer switch.
If you can, check for tightness on all of the transfer switch connections.