You can pick up Kornati passes at ACI Vodice and ACI Zut
But if you are clever you can actually sail through without needing to pay
If you are going N to S then overnight off Otok Katina between Kornat and Dugi Otok. There is a little konoba with moorings which is actually outside both National Parks and you can anchor
in the next bay too. Then sail down through the Kornati chain to Zirje, Kakan or Kaprije where you can pick up a mooring
buoy. Or do the reverse is S to N.
Of course if you want to stay the night then you will have to get the permits. If you don't want to stop off and pay in advance, which is cheaper, then you can pay the NP Rangers when they come round to check passes. There is also the NP Offices on Smokvica and mid way up Kornat where you can get passes.