No, the Avocado mattress should not be flipped. The Avocado logo should always be right-side up.
Avocado mattresses are designed with a single comfort layer on one side of the mattress. The foundational side does not have comfort materials and is not designed for sleeping on.

With that said, you SHOULD rotate your mattress (head to toe). Rotate the mattress at the 6 month mark and then every 12 months thereafter. This helps to ensure that the mattress wears evenly.