I want to get to Sulawesi (Makassar I suppose) from Flores.
Is there any direct flight or ferry?
Or must I go first to another location (i.e. Bali) to take a flight from there?
Any budget option appreciated.
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It's hard to prove a negative, especially in a country like Indonesia where airlines pop up and disappear overnight, but no, I don't believe there are any direct flights or ferries.
There are three airports of any size on Flores: Komodo/Labuanbajo (LBJ), Ende (ENE), and Maumere (MOF), none of which serve Sulawesi's largest city and geographically closest airport in Makassar (UPG). It's thus highly unlikely that there are any direct services, and you're probably best off detouring via Denpasar-Bali (DPS), which is well connected to all four and a bunch of other airports in Sulawesi as well:
(courtesy Great Circle Mapper)
Have you tried the Indonesian travel website http://www.tiket.com? It looks like you can fly on Wings from Maumere to Makassar for about $175 (stops in Denpasar).
I don't think there's a direct flight from Flores to Makassar. I don't know where in Flores will you start your journey, but here is a list of airports (bandara) in East Nusa Tenggara, of which 4 are in Flores. Here is the international airport in Makassar. There is a table showing which airline flies to which city.
You could look for possible connections in websites such as Skyscanner or Kayak, but I think not all options are shown there. I usually use a local website, Traveloka, or direct in the airline's website. My favorites are Garuda Indonesia and Citilink (LCC, a subsidiary of Garuda).
PS: Just noticed that this question is already 3 months old. I hope you've already figured it out.