There isn't a specific, commonly used term for flying beneath the moon and stars. Here are some options, depending on the context and desired effect:

Descriptive:

* Flying under the night sky: This is the most straightforward option, clearly stating the location.

* Soaring beneath the celestial tapestry: This is a more poetic option, emphasizing the beauty of the night sky.

* Cruising through the starry void: This option is more evocative, focusing on the vastness of space.

Figurative:

* Dancing with the moon and stars: This option implies a sense of joy and freedom.

* Whispering through the cosmos: This option evokes a sense of quiet and mystery.

Ultimately, the best phrase depends on the specific context of your writing or speech.