Can I quit flovent cold turkey to wein myself off of it?

No. Wean gradually to lowest dose. Albuterol use will be your guide (if using it less than 2 time per week daytime or less 2 times per month at night then your asthma is controlled.) decisions not to use Flovent depends on use if albuerol for rescue and lack/prescience of symptoms. Talk to your doctor.
Why. If you never experience night cough, day symptoms and haven't needed your rescue inhaler in months it might be something you can try.But if you have real asthma and any symptoms it would be a bad idea. Daily inhaled steroids (flovent) is like a vitamin for asthma sufferers. Asthma is marked by chronic increased lung sensitivity & it keeps it in check. It can get out of hand & lead to poor control.