Have a pirate speak contest to see who can sound the most like one of the pirate characters in the book. Long John Silver. The performers will read from a passage in the book and throw in a few "arrs," "avast me hearties," and "Jim Lads," basing the accent they use on that used in the movies and generally expected from pirate rogues.
If you want to have singing in your Treasure Island themed talent show, provide the performers with a list of old seas shanties that they can sing. Some selections might be What Do We Do With a Drunken Sailor, Sixteen Men on a Dead Man's Ship, or some of the tunes from The Pirates of Penzanze like "I Am a Pirate King."
Another type of act your performers can do is sailor dances. Sailors and pirates are well known for frequently performing various dances and jigs, such as the Hornpipe. Alternatively, allow the performers to present the formal dances a pirate might have encountered while on shore leave, such as English Country Dances.
The talent show performers can as a group present a particular scene from the novel, such as the scene in which Blind Pew arrives to give Billy Bones the black spot. Whichever scene you choose needs to be all in a single room so you don't have the change scenes and props. The judges can then grade each performers work separately to assign points.