The rules for being underwater apply an attack penalty on a slashing weapon, such as a whip, but you can still use them. If you can attack with a whip, you can crack it, so even assuming we give that bit of fluff more weight than I think it’s due, it still works underwater.
Magic missile, of course, works; the only sort of magic to have much difficulty in water is fire effects, and magic missile is not that.
And from a game perspective, whips are terrible, atrocious weapons, and the legacy rules amount to nothing more than an overcomplicated trap. Using either is a bad idea for mechanical effectiveness; combining both together is a particularly poor one. So any character using Flay simply needs all the help they can get; adding an unnecessary nerf like failure to work underwater is a very bad idea for the game.