I am very stupid at times. My top coop always gets flooded. So I put in a basic drainage system. I move all the girls down garden to the bigger coop until the water has drained from the top. Bottom coop never gets flooded. I have NEVER even thought of sand. Where I live in the UK we suffer from floods and we use sand bags to keep the water out. As homer simpson would say: DOH!
It's probably too late to build the base of the coop properly, but you could dig out some soil around the perimeter of the coop, and but in french drains and gravel, and then direct the water flow away from the coop. It might keep it from flooding, and would at least transport the water away more quickly. If you can do the same under the run, it would be good too.
You might want to read this. It’s about runs but a lot of it applies to coops as well. Pat’s Big Ol' Mud Page (fixing muddy runs): https://www.backyardchickens.com/web/viewblog.php?id=1642-fix-a-muddy-run Why is the coop getting wet? How does the water get in? There are two basic parts of a dry coop. First is to keep the water out to start with. You might want to address that part. Pat’s article might help you with that. Gutters and downspouts to direct water away from the coop, berms or swales to keep water from running in, shutters or some kind of rain guards on windows or ventilation. It just depends on how the water is getting in. The other is what you addressed, get the water out once it gets in. A working drainage system is great as long as the water has a place to go. I’d guess since it is your top coop you managed that. If it has enough ventilation it will dry out faster. Bedding makes a difference too. Organic material like wood shavings or straw tends to hold moisture. Sand will drain quite well as long as the water has a place to go. Another trick is to scatter a treat they have to scratch for like maize so the chickens turn the bedding for you. That helps it dry out.