Didn't seem like both f16 pilots called the Other Cookie?
Only one of the two F-16 pilots speaks dialog in the movie. The pilot who speaks calls his wingman: "Cookie."
The speaking pilot was ultimately shot down. When this happens, he says, "I'm hit, Cookie! I'm hit! He blew my [expletive] wing off! This is Little Brother One, I'm ejecting . . . "
Therefore:
The speaking F-16 pilot's call sign is: Little Brother One The 'other' F-16 pilot's call sign is: Cookie