Here is the first of the flight summaries for 2019 – from the UK. There are also charter flights from Dublin to Rhodes, but as far as I can see it isn’t possible to book flight-only on them. Note that there are currently no Norwegian flights showing, last year these showed up later, and Ryanair added more than were visible at first.
Other comments that I’d ask readers to note are:
Times for Thomas Cook and TUI are quite likely to alter between now and the day they operate as the slots are not finalised yet, they may also subcontract some flights – they usually do.
The continued lack of information about air travel arrangements after Brexit means that the whole thing is more problematic than usual. My best guess is that nothing much will change on the flight or immigration from for 2019 – after that anything is possible.