Background:
The Soar rules actually restrict the use of Soar to ‘outdoor encounters’. Which means that, strictly speaking, Soar cannot be used during an Island dungeon level! Is that correct?
Note that this could greatly ease the problems with some of the island levels where Soaring Leaders can be near-impossible to get at and kill (especially combined with Scrub).

Question:
Q. Do creatures with the Fly ability also gain Soar in an Island level of a SoB campaign? Do creatures with the Soar ability get to use it in such a level?
A1. Yes they do, since there is nothing to restrict their movement in the air above an island.
A2. No they don´t. An Island level is still part of a dungeon, so all rules pertaining to dungeons still apply.

Flavorwise, monsters should get Soar on Island levels.

However, the difficulty of some Island levels becomes so great that for the balance of the game, monsters should not get Soar on Island levels.

Hard to decide, but if I had to, I would decide in favor of game balance.