June is a good time to travel trough the centre but can be very cold (around 13C) during the day, night time down to zero.
Dalhousie Springs has an airstrip and some very warm thermal pools which are great for a visit in June, not much good any other time of year.
Flying weather should be fairly good, although be prepared if there is low cloud it might hang around for a few days.
Kings Canyon is less than 20 mins from Ayres Rock, would recommend overflying 'Gosses Bluff' a little north of Kings canyon.
Cheers, HH.