Hi, welcome to the forum. Glad you joined.
It sounds like your concrete slab holds water instead of drains, which could be a real problem. Is water getting in there? If you can keep rain, snow, and groundwater run-off out, your waterer isn't leaking somehow, and you don't have a lot of condensation you may be able to handle it but where water collects can be pretty challenging. The problem is not that your coop floor is concrete, the problem is that it holds water.
Adding pea gravel will not choke the chickens, they'll use the smaller bits as grit. The issue if your slab won't drain is that water will collect under whatever you put in there and manure will also go down to the water. It will be like a bathtub full of gravel, manure, and water and likely go anaerobic. That's when it really stinks. As long as it holds water you probably are not going to come up with a permanent fix, you will sometimes have to clean it out and gravel can be heavy.
Another way to get moisture in there is the poop. If poop builds up it can retain moisture and never dry out. Dry poop isn't your problem, it's when it stays wet that it starts to stink. How many chickens you have, how big the coop is, and how much they poop in there will determine poop load. The more they are in the run the less they are pooping in the coop. But even then they poop a lot at night. Using a droppings board can greatly reduce the poop load which may help you. It doesn't matter if your coop floor holds water or drains, if the poop gets too thick it holds moisture.
Think of bedding as a diaper. It dries out the poop and keeps things under control as long a it stays dry enough to absorb moisture. Once it is wet though it quits working. If the bedding is sitting in a pool of water it will not dry out.
It's not always easy but if you can keep water out of your coop I'd suggest you go with a fairly thick bedding. Everyone has their favorites but I'd think in terms of wood shavings, hay, straw, or maybe wood chips. A lot of what is best depends in where you are and what's available at a reasonable price. If it has a little moisture in it this can turn into a compost pile, this is often called the deep litter method. If it gets too wet it will start to stink just like a too wet compost pile will. If it is too dry it will not compost but will act as a diaper to absorb the moisture in poop and keep things nice. This last is how I do mine. It stays so dry, I use droppings boards to reduce poop load, and my chickens are hardly ever in the coop during the day so I clean mine out once every three or four years. Very few people can go that long.
If you cannot keep water out and it collects under whatever you put n there you will probably be stuck cleaning it out on a regular basis. I don't know how big that coop is or how hard or often that will be.
Can you drill holes through that slab in the low spots so water can drain out? That might be worth the effort.
The problem you are describing is the water. The poop build-up is a different issue. Your solutions are to keep it out to start with or get rid of it after it gets in. Good luck!
