We have direct flights in high season to Santorini (April-May / September-October) from several french citiesand also from Amsterdam and London.
Arline companies are the following ones - not exhaustive list - : Air France, Aegean Airlines, Olympic Air, Athens Airways, Greek Travel Pages, Sky Express, Lufthanza, Astra Airlines, Swiss, Edelweiss Air, Air Maroc, and the low cost ones (Transavia, Easyjet, Ryanair, Volotea, Vueling, Jet4you, flybe,)
Please check directly wiith your Airport
You can also fly directly to Athens and take a Ferry boat or Express ( hydroplanes called hydrofoil, or fast catamarans) from the Port of Piraeus.
If you do not find a cheap flight to Santorini, please consider the way to come first to the Island of Crete to Heraklion (HER) and every morning, two fast boats (2 hours) go to Santorini.
Links: www.seajets.gr and www.hellenicseaways.gr