I want to create a custom Alexa skill to create appointments in my company. The clients would install the skill and Alexa would tell them the available hours for them to choose.
This is achievable with a custom skill. Do you already have a database from which Alexa can pull the available slots?
If so, you can query that database from your Lambda function (or custom endpoint) and update the time slots according to the user interaction.
I would handle it with at least 2 intents:
Triggered when the user asks for availability.
Triggered when the user decided (and confirmed) the wanted time-slot.
If you don't already have own a database, please have a look into the Alexa-Hosted skills:
This gives you access to an AWS Lambda endpoint, an Amazon S3 bucket for media storage, and an Amazon S3-backed key-value table for managing session persistence.
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