What is this fluffy stuff?

Yikes!  I have no idea, but you are right, it probably isn't good for your chickens.  I wonder if  diatomaceous earth might not help dry the area out and keep stuff from growing without introducing something harmful to your run area.

I would originally have thought some sort of mold growth from spoiled food, but its interesting that none is growing around the feeder on the left hand side of the picture, or the visible food on the ground over there. Hope someone else can help.

I looked it up on the Internet, near as I can tell it is some sort of fungus or mold. I would put down sand mixed with DE and see if that clears it up. The sight said to use insecticides, but you can't do that in the coop. If that dose not help, maybe you can call the county agriculture department see if they have a solution. I am sure once the rain let's up, the ground dries up, it will go away.

That looks like some kind of mold.i would keep the birds away from it. (by the way, I love the hen creepily staring out the coop window )
It should dry up eventually. DE would help too.

I have never seen that before, but want to say I love the chicken looking out the window of the coop in the second picture. LOL

It is a mold.  Spray the area with straight white vinegar.  That will kill it for awhile then cover the area to keep it dry. Add sand as needed.   The spores are sure to irritate your chickens and your lungs as well.  Molds can be very BAD.  Gloria Jean

That stuff is spooky  strange! I  think  the white vinegar idea is a good one to try  and i dont think it can hurt the chickens at all,I read to used vinegar  or slat to clean  humming bird feeders  and I use it for my  chicken  waterers   Salt will work  as it kills plants which is what fugus is but not sure salt is good for birds as it willbe in the ground forever after.Good to use to clean things though.They use salt now for swimming pools as an alternative to the clorine type pool  cleaner.And yes sand ...it shouldnt grow back on sand and better for the chicks feet than patio blocks.

Wow, that is intense growth.  If you had just shown the picture I would have said it was either a silkie who had been demolished by a predator or cottonwood (I do live in Kansas so we see a lot of that at certain times of the year).  Its hard to believe mold could grow to that quantity in that short an amount of time!