I cant for the life of me find the answer to how long after my chickens run over one area can I use that area again while keeping the pasture healthy?
I suggest you start with a small number of meat birds (1 to 3 moveable pens) the first year, and watch how your own pastures perform. You can use that to work out how much to expand in future years. You can almost certainly go over each area at least once a year, given that you are calling it "pasture" instead of "desert." You can probably do it more often than that.
When you try it, you might find something like one of these possibilities:
You might move each patch of meat birds onto a fresh spot every day for their whole life, then be able to start the same pattern again with the next batch. Or you might be able to run the first batch back over some of the same areas they already used. Or you might need to move the second batch over fresh ground, because the first ground isn't yet ready again.
In general, chickens eat grass, scratch, and poop. Too much of that kills the grass. The right amount makes the grass grow faster. Grass also grows faster at the right temperature, with the right amount of rain. So you can probably re-use the same area sooner at some times of the year, and wait longer at other times of the year.
You probably don't want to raise meat chickens in the middle of winter, and maybe not in the middle of a hot summer (depending on climate.) So the whole pasture would get a rest at that time, but the grass won't be growing well anyway when the temperature is too cold or too hot.