Mykonos remains one of the Aegean's stubborn holdouts against nonstop long-haul service, which means there is no single carrier offering business class from Fort Lauderdale to Mykonos on one ticket — the smart routing runs through a major European gateway, with a connection onto Aegean Airlines' seasonal Athens–Mykonos hop. British Airways via London Heathrow remains my preferred build, pairing a Club Suite experience across the Atlantic with a same-alliance-adjacent connection into Athens before the short island jump. Lufthansa's Frankfurt or Munich routing is the other viable path, and depending on aircraft assignment you may land the newer Allegris cabin on the transatlantic leg — worth checking before booking, since not all FLL-Frankfurt equipment has been retrofitted yet.
Having threaded this itinerary more times than I can count, my advice is to treat the Athens layover as a feature, not a bug: build in enough connection time to clear passport control comfortably, because Aegean's Athens-Mykonos service operates from a separate check-in process that rewards travelers who arrive with margin rather than rushing a tight transfer. Aegean itself doesn't fly business class in the traditional wide-body sense on this short hop, but its business cabin on the A320 family offers blocked middle seats and a proper meal service that feels indulgent for forty-five minutes in the air — a pleasant surprise for those expecting a bare-bones regional product. Seasonality matters enormously here: Mykonos essentially shuts down internationally outside the May-through-September window, so your business class positioning flights need to align precisely with the island's operating calendar.
Because this itinerary depends on stitching together long-haul business class with a seasonal regional connection, fares swing widely based on both legs' availability rather than one carrier's pricing whims. April, May, September, and October reward patience and flexibility, but the compound nature of this routing means setting continuous fare alerts is far more valuable here than on a simple nonstop — small shifts in either segment can meaningfully change your total outlay.