"Eating on the fly" or "grabbing a bite" are both idioms that can refer to eating quickly or without much thought or planning.

For example:

"I don't have time to sit down for a proper meal, I'll just grab a bite on the go."

"I was in such a rush this morning, I just grabbed something to eat on the fly before heading out the door."

These idioms imply that the person is not taking the time to sit down and enjoy their food or pay attention to their diet, but rather just trying to get some sustenance as quickly as possible.