if you can get some vinyl for free or close to free, it might make it a bit easier to clean and help reduce wear on your plywood floor, and so be a good choice.
If you want to use anything to clean the coop (like a pitch fork or very pointy rake) you might want to avoid vinyl since something pointy used with force would tear it up quickly.
I think painting the plywood with paint from the "oops wrong color" at your local hardware store, or using extra paint from your house is a great way to help protect the plywood a little more.
the sand will wear through the paint layer over time, but I don't see that as a big problem. The sand would do the same with vinyl (slowly wear through the top layer), but if the vinyl is free or cloe to free, then it would be a good way to protect the plywood floor.
If you have a concrete slab, and want to use sand, I wouldn't bother putting any paint or vinyl on it.
Thanks for the advice! My husband's buddy has some free extra laminate tiles that he gave me. They are two different colors, but they don't have to match since they will be covered with sand! I will go ahead and put them in. Thanks!