Is it possible to travel to Koh Samui right after quarantine in Bangkok, and what documents do I need?

Book a flight with Bangkok Airways to Samui straight after the Quarantine No problem at all

I know the 19th seems close, but at the rate things are changing right now it's simply impossible to get an answer on this that will still be accurate by then. I imagine within the next week or so we will see how things start to shape up with the restrictions and flight schedules will begin to settle down after the airlines decide who will and who won't be flying anymore.

I think you'll be able to find a flight, and your ASQ discharge papers should be good enough to get you past any checks based on previous restrictions. I would advise against purchasing a flight if you haven't yet, until we have a better idea of what's going on.

As far as I'm aware, it has been possible once you leave Quarantine (with all your paperwork in order) to travel directly to Samui. That said, I understand Buses to the south have been cancelled and you may want to check if flights are still going to Samui (or Surathani). Best of luck