Your sentence is almost correct! Here's a small change to make it sound better:
Original sentence: The kestrel flaps its wings fast to hang in the air and then it swoops down on a mouse.
Corrected sentence: The kestrel flaps its wings quickly to hang in the air, and then it swoops down on a mouse.
Explanation: Instead of 'fast,' we use 'quickly' to describe how the kestrel flaps its wings. Also, we add a comma before 'and' to connect the two actions more smoothly.