What is the most recent common ancestor of birds and flying insects?

It should be obvious that birds and flying insects had quite different common anscestors

Birds are vertebrate animals, insects, invertebrate.

A common ancestor for these would go way back to urbilaterian, ergo Jaz and Bulldog are both likely correct.

An "urbilaterian" from before the time that the deuterostomes and protostomes diverged.

The most recent common ancestor probably lived even before the Cambrian explosion 543 million years ago.