I don't know about Cook County, but you might be able to search online for the FPDCC regulations.
I got kicked out of a DuPage preserve last year, and I went home and looked up the regulations online. I was so sure I was right about being able to fly that I took them back to the park and showed them to the cop! The Dupage regulations state that you can't take off or land
by kite, glider, ultralight, airplane, etc., but they do not specifically state that you can't fly kites. After I showed the regulations to the officer, he agreed that he should not have asked me to leave. I think he was new and therefore didn't really know the regulations in detail. So, I think if you have the regulations on your side (and have a copy) and are polite, you might be able to keep flying.
Of course, all this assumes you aren't flying power kites big enough to take off or land!