It takes 24 hours underwater to drown a flea! This is an interesting question and a pertinent one because cat owners sometimes like to kill fleas by drowning them. There are two aspects to the question. If you place a flea onto water they don't sink into the water. Therefore they do not drown this way. Fleas are too light to break the surface of water. And they are covered in a water repellent wax. A flea left on the surface of water in a bowl will eventually starve to death because they can't jump out, but not drown.
If you force a flea underwater and hold it there for about 24 hours they would drown. Apparently it takes much longer to drown a flea than you might have imagined. Forcing a flea underwater for 20 minutes will not kill them. In fact a flea submerged for 12 hours may appear dead but will reanimate itself once removed. After 60 minutes or so they are revived. If a flea is underwater for up to 20 hours they can still revive themselves but it takes about 4 to 5 hours.
If you are flea combing your cat and you catch one, my preferred method of killing is to use my thumbnail to squash the flea against the comb. If the comb is a metal one with a ridge where the combs enter the plastic handle you can squash them against that ridge. It is satisfying because you can hear the exoskeleton pop. This method may be too grizly for some people. It gives me pleasure because I hate the bastards. But if there are a lot of fleas this method is unworkable. You'll need an insecticide but use it with extreme care please.
P.S. Fleas have flat bodies which makes it easier to move around their host in that forest of fur!
Sources: various and on the internet.