It will be very hard to pick specific KPIs but you can make sure that you don't incentivise behaviour that results in a negative impact on safety. Try inverting the question. 'What behaviour are we currently incentivising that will result in unsafe behaviour?'. For example if you tie your staff's pay directly to something like on time performance you will inevitably get people cutting corners to get the aircraft away on time.
Safety is an outcome of decisions. Using metric such as incidents reported is always fraught with danger as other posters have already said. My experience is that the best way to encourage safe behaviour is public support for staff who make a decision in the name of safety that will obviously cost the company some money. This is particularly he case if the person has personally made a mistake which leads to the situation in the first place (eg service a gearbox with the wrong type of oil) but their decision to put their hand up prevents a greater risk.