Why do you want 00 flour? Is it a gluten factor?
If you put AP flour into the food processor, you will definitely have finer flour, and flour in other places, but it will still have the gluten level it had before you processed it.
If you are searching for a finer flour with a lower percentage of gluten, how about mixing cake/pastry flour with the processed AP flour?
"As a girl I had zero interest in the stove." - Julia Child
This is real inspiration. Look what Julia became!