Here's a breakdown:
* No se aflija: This literally means "Don't be afflicted" or "Don't worry". It's a common way to reassure someone.
* acabo de bromear: This translates to "I just joked". It indicates that the previous statement was meant in a humorous way.
So, the whole phrase is meant to ease any tension or worry that might have arisen from a previous statement that was intended to be a joke.