Why dont you just add sand on top of the existing soil? It's much easier and you'll be elevating your pen while the yard floods if there's heavy rains. Besides, your soil is probably already waterlogged like ours and it wont take long for flooding to occur. If you've had a lot of rain like we have, I'd bet your water table is just a few feet down in the ground.
Earlier this year I hauled in a total of 7 pick up truck loads of sand, refreshing both pens. I'm glad I did. It has been raining practically every day for the last 4 months. I'm not talking about 'splash and dash' showers neither, deluges of rain for long periods of time. It was alot of hard work doing it myself, but it paid off.
While our yard floods, the sand in the pens have held up and doesnt flood. Sand doesnt wash away like dirt, it soaks up water, dries quicker than mud, and helps deter parasites. There are no nasty mud holes for chickens to drink out of neither.
If anything, hard rains beat the sand down into the soil, eventually replenishment is necessary like I did earlier this year. Here, it costs $25 for 1 cubic yard of sand.
I keep my birds penned 98% of the time. Refreshing sand with another layer of sand helps prevent worm infection with birds kept on the same soil for long periods of time. However, I worm my birds monthly so it's not really an issue for me, but I refresh sand at least every 6 months or so anyway. it's easier to scoop poop with sand, and I do it 2 or 3 times a day.
I use the soiled sand for filling in ruts or holes in the yard due to rain washouts in different areas of our yard.
I have tarps over my main coop and smaller coop, and both coops are elevated above the ground. I have a jury rigged gutter running off the main coop with a 4" corrugated flexible pipe attached directing rain water off the roof out into the yard.
I'll be replacing the tarps and doing some caulking early this coming week when we're supposed to get some drier weather for a few days.
Our weatherguessers here are the worst I've ever seen with their forecasts. Unfortunately they cant forecast yesterdays weather much less tomorrows. So, we'll see how it goes.