We searched up and down on the internet and in the end, we booked our flight from Miami to the Turks on American Airlines. They are the only airlines really that fly there.
I can tell you now tho that there are two flights on the 30th, 31th and the 1st.
The 2:35pm flight IS ALL BOOKED UP however you might still be able to get a ticket with Expedia or Priceline if you can afford to pay $2,000.00 plus. Mind you, they were originally $487.00 with the "discount" but of course, everyone wanted that flight in instead of the 2nd one which doesn't arrive in the Turks until 8:35pmish and by the time you leave the airport and get to Club Med, you'ld be checking in pretty late and you'ld miss the whole first day.
If you fly in on the 31st to the Turks like us, you will simply have to find a place to stay for the night cause Olivia does not have any "Pres" just "Posts".
I found a great deal from PDX to Miami on United Airlines with just one stop in between.
You can email me if you want or need more details!
Elita, the Chef