Are there nonstop flights from Athens (ATH) to Skiathos (JSI)?

Yes. Sky Express (Greece), Olympic Air fly this route. Flight time is about 40m.

Athens → Skiathos

Athens Eleftherios Venizelos International Airport (ATH) to Skiathos Island National Airport (JSI)・143 km

Nonstop flights available (2 airlines). Flight time about 40m. Nonstop return flights also operate.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.