@Ian W:
Useful summary here:
A Super Solar Flare - NASA Science
In short, it seems that satellites and broadcast communications may be affected by a Carrington Event, but shielded electronics of the kind used on aircraft would have a reasonable degree of protection.
It would have a far less disruptive effect than the much-feared electro-magnetic pulse (EMP), but given that the only thing that can trigger one of those is a nuclear detonation in the Earth's atmosphere, I'd be inclined to suggest that should one of those be encountered, an EMP messing with your electronics would be the least of your worries!