Oy, we're probably going to have that here soon -- we have SOOOO much snow on the ground and it's gotta melt SOMEday (in fact we're expecting 1/2"+ of rain tonight and tomorrow, don't know think that will be the definitive spring thaw tho). You certainly have my sympathy
First, is there anything you can do to route the water elsewhere -- run downspout outflow thru drainpipes or etc, dig shallow trenches leading off to lower ground, etc. Make sure a gutter or downspout hasn't come down (fix it of course if it has).
Second, see if you can score some pallets. Businesses often give 'em away for free, do some phoning around. You can stack pallets as much as several layers high if necessary, put old carpeting on top of them (or a tarp over top of opened-out cardboard boxes, if you're really desperate), bedding on top of the carpeting, and your chickens are up out of the flood.
As SOON as the flood is over, remove the soggy litter. You can spread it out to dry in the sun and depending on how nasty it was before it got wet and how fast you can get it to dry out you might even be able to reuse some or all of it, esp. if it can go in a covered outdoors area. You don't want to leave it in the coop any longer than avoidable, tho, since it can be a mold farm and will encourage the wood of your coop to begin rotting. For now, though, it is a good thing, as it will sop the water up and keep the water from going even LESS desirable places.
GOod luck,
Pat