Flips are explicitly whole egg cocktails. If you're not using the yolk, you're not making a flip.
If you try to use aquafaba to replace the egg in a flip recipe, you'll end up with a different drink because you won't have the flavour of the yolk.
Flip – An entire egg
Nog – An entire egg plus dairy
Sour – Egg white only
Fizz – Egg plus carbonation
Optionally, but less common: Silver Fizz (egg white), Golden Fizz (egg yolk), Royal Fizz (whole egg) + carbonation.