I think the rainbow system does not have to mean a new uniform. On today's carriers the clour coding works by way of a coloured vest worn over the uniform. So if it is implemented for the Akira-class (and other carrier-cruisers) the flight deck crews would just wear a vest over their standard uniforms. Alternatively they could wear variants of the engineering coveralls in different colours.
One thing though, the rainbow system was invented so that the Air Boss could see where everyone was on the open flight deck from his vantage point high up on the island of a seagoing carrier. Onboard a starship, the flight deck is more confined and with modern technology, the Air Boss can actually "see" everything on the flight deck on the flight deck level so the colour coding to identify personnel may not be required any more. Or the communicators can trasnmit their locations to a board in flight ops where they can be kept tack of on an individual basis.
Arise, arise, Riders of Theoden!
Fell deed awake: fire and slaughter!
Spear shall be shaken, shields be splintered,
a sword-day, a red-day, ere the sun rises!
Ride now, ride now! Ride to Gondor!
Theoden King: The Return of the King