The most direct route to getting to Ireland and the start of the Dingle Way is to fly to Kerry Airport in Faranfore which is 18km from Tralee. Due to the size of the airport however there are only a limited amount of flights that land here.
Ryanair fly to Kerry Airport from Dublin, Frankfurt, Luton and Stansted. Aer Arann fly from Dublin, Manchester and Lorient.
Cork Airport and Shannon Airport are the next closest both being around 120km from Tralee. There is a broad range of incoming flights landing at both of these airports.
If you are still finding difficulty in sourcing a flight from your nearest airport then Dublin Airport may be able to provide you with an answer. Be warned that Dublin is over four hours from Tralee by car and it may be worth investigating other airports within your own country to see if they serve Cork or Shannon.