Wait, could you clarify what the support system is for the floor? How many cinderblocks is it up on, placed where? If it has none in the middle (just at corners or edges) then you need more than just another sheet of plywood; if you have lots and lots of them all across the middle you may not need anything more than you've already got, although rats might be a concern.
As far as the original question goes, plywood is a fine flooring with shavings (or whatever) put onto it. I would suggest painting or polyurethaning the plywood as it makes it EVER so much easier to clean -- and sometimes the chickens WILL scratch bare spots in the bedding which will then allow the plywood to get directly pooed-upon, so cleaning really IS an issue. But if you do that, it makes a plenty good floor.
Good luck, have fun,
Pat