I am building a Alexa Skill Set which returns list of events. I would like to my skill to book an appointment for selected events by the user.
If the user says "Alexa book appointment for the last event", I want my skill to handle it and book an event in the linked calendar.
How do I get access to the linked calendar within my skill?
For this, you need to get access to the user's calendar, which you can get via account linking. You can find more information by Amazon here: Link an Alexa User with a User in Your System.
In the account linking process, you then need to use Google Sign-In. Here's another helpful link for Google Calendar specifically: Authorizing Requests to the Google Calendar API.