I think using pallets as a temporary solution to keep the chicken up and out of the muddy water is a great idea.
I think a longer-term solution would be to build up the coop and/or chicken run floor. I don't have a flooding problem, but I dumped in all kinds of organic materials into my chicken run, including wood chips, leaves, dried grass, etc... I have about 12-18 inches deep litter depending on the time of the year. If my chicken run ever did flood, I would never notice it unless it was higher than that 12-18 inches of litter.
A few years ago, I watched a YouTube video of some guy down in Texas who was dealing with a couple of inches of flood water in his chicken run. He kept dumping in wood chips until the flood waters were no longer an issue for him. I suppose you could use pallet wood as a barrier around the coop or chicken run to hold in all those wood chips or other litter that you might use to raise the level of the floor. You don't want all that hard work to wash away.
The chickens would also enjoy scratching and pecking in the deep organic litter whereas there is not as much to do standing on pallets. My chicken run litter at 12-18 inches deep is full of worms and bugs. Keeps my chickens happy all day long scratching and pecking in the compost for things to eat.