In order to progress to the next Chapter or scene, you need to ensure that you have collected enough badges and prestige. 

1. Badges – you need to have won 20 badges in the previous chapter and to have completed the final scene

2. Prestige – you need to add enough buildings or decorations to your island

This last requirement applies only for Computer Users who are playing with Friends via Facebook:

3. A Flight Crew – you will need the help of 3 friends to fly to the next chapter. 

To ask for help simply send your friends requests from your 'next chapter travel' pop-up.