I want to create the dashboard dynamically using dynamic MySQL query. Is it possible?
Your title asks if you can create a QuickSight dashboard programmatically. The answer is no. The only QuickSight APIs are for managing Users and Groups.
Your question then asks if you can use Dynamic MySQL queries. Using a SQL Query - Amazon QuickSight says:
When creating a new data set based on a direct query to a database, you can choose an existing SQL query or create a new SQL query.
That might be what you seek.