On the first day of the tour, you need to be in Demre. Therefore, you can come there the day before from Antalya or Dalaman, the journey takes 3-4 hours by public transport. You can also arrive in Demre early in the morning on the first day of the tour, but it might be challenging as the day is busy.
It's better to fly back the next day after the tour ends. The journey from Kaş to Antalya or Dalaman takes 4 hours by public transport.
You can buy air tickets without checked baggage and only take carry-on luggage, as you only need to bring comfortable summer clothes :)